BEGIN:VCALENDAR PRODID:-//eluceo/ical//2.0/EN VERSION:2.0 CALSCALE:GREGORIAN BEGIN:VEVENT UID:d891e525fced25d2558a53a25008b776 DTSTAMP:20260607T164058Z SUMMARY:ETH – Hong Kong – Imperial Mathematical Finance Workshop DESCRIPTION:This workshop\, held during the week of June 17\, 2024\, will b ring together leading research groups in Math Finance from three of the wo rld’s financial centers. The workshop will feature talks by academic res earchers from Imperial College London\, ETH Zurich\, Chinese University of Hong Kong and the Hong Kong Polytechnic University.\nParticipants\nImperi al:\nJohannes Muhle-Karbe\, Antoine (Jack) Jacquier\, Eyal Neuman\, Harry Zheng\, Yonatan Shadmi\, Pietro Siorpaes\, Lukas Gonon\, Yufei Zhang\, Dav id Itkin\, Ofelia Bonesini\, Ioannis Gasteratos\, Damiano Brigo\, Mikko Pa kkanen\, Philipp Jettkant\, Anthony Coache\, Nicola Muca Cirone\, Konrad M üller\, Will Turner\, Francesco Piatti\, Nikita Zozoulenko\, Yun Zhao\, S turmius Tuschmann\, Robert Boyce\, Guangyi He\, Ruben Wiedemann\, Joseph M ulligan.\nHK PolyU:\nMin Dai\, Kexin Chen\, Zhaoli Jiang\, Jiacheng Fan\, Shuaijie Qian (HKUST).\nCUHK:\nNan Chen\, Chen Yang\, Xuedong He\, Lingfei Li\, Yanwei Jia\, Dohyun Ahn\, Shuoqing Deng (HKUST).\nETH:\nBeatrice Acc iaio\, Walter Farkas\, Dylan Possamaï\, Martin Schweizer\, Josef Teichman n\, Robert Crowell\, Jakob Heiss\, Songyan Hou\, Evgeny Kolosov\, Benjamin Kotlov\, Florian Krach\, Daniel Krsek\, Patrick Lucescu\, Tengyingzi Ma\, Marco Rodrigues\, Mateo Rodriguez\, Chiara Rossata\, Daria Sakhanda\, Qin xin Yan.\nSchedule\n\n\n\n\n                                          Monday June 17\n\nTuesday June 18\nWednesday June 19\nTh ursday June 20\n\n\n8:30-9:00\nRegistration\n9:00-9:25\nXuedong He\n\nMikk o Pakkanen\n\n\n9:00-9:10\nOpening remarks by Johannes Muhle-Karbe\n9:25-9 :50\nJohannes Muhle-Karbe\nJiacheng Fan\nLingfei Li\n\n\n9:10-9:35\nMin Da i\n9:50-10:10\n                                      Br eak\n\n\n9:35-10:00\nJosef Teichmann\n10:10-10:35\nEyal Neuman\nYonatan Sh admi\nShuaijie Qian\n\n\n10:00-10:25\nNan Chen\n10:35-11:00\nYufei Zhang\n Zhaoli Jiang\nPietro Siorpaes\n\n\n10:25-10:45 \nBreak \n11:00-11:10\n                                      Break\n\n\n10:45-11 :10\nShuoqing Deng\n11:10-11:35\nAhn Dohyun\nOfelia Bonesini\nPhD talks Se ssion 5\n\n\n11:10-11:35\nDylan Possamai\n11:35-12:00\nIoannis Gasteratos\ nPhD talks Session 3\n\n\n11:35-12:00\nDavid Itkin\n12:00-12:25\n\n\n\n12: 00-13:15 \nLunch\n12:25-13:40\n                                      Lunch\n\n\n13:15-13:40\nKexin Chen\n13:40-14:05\nPhD Talks Session 2\nLukas Gonon\n\n\n\n13:40-14:05\nHarry Zheng\n14:05-14:30\nChen Yang\n\n\n\n14:05-14:20\n Break\n14:30-14:45\nSocial Program\nBreak\n\n\n\ n14:20-14:45\nYanwei Jia\n14:45-15:25\nPhD talks Session 4\n\n\n\n15:10-15 :25 \nBreak\n15:25-15:35\n\n\n\n\n15:25-15:50\nAntoine (Jack) Jacquier\n1 5:35-16:15\n\n\n\n\n15:50-16:30\nPhD talks Session 1\n\n\n\n\n\n\n\n\n \n PhD Talks\n\n\n\n\nFirst Name\nFamily Name\nInstitute\n\n\n\nSongyan\nHou\ nImperial\nSession 1\n\n\nRobert\nCrowell\nETH\n\n\nGuangyi\nHe\nImperial\ n\n\nJakob\nHeiss\nETH\n\n\n______________________________________________ ___________________________________________\n\n\nRobert\nBoyce\nImperial\n Session 2\n\n\nSturmius\nTuschmann\nImperial\n\n\nFlorian\nKrach\nETH\n\n\ nNikita\nZozoulenko\nImperial\n\n\n_______________________________________ __________________________________________________\n\n\nPatrick\nLucescu\n ETH\nSession 3\n\n\nTengyingzi\nMa\nETH\n\n\nChiara\nRossato\nETH\n\n\nRub en\nWiedemann\nImperial\n \n\n\n_________________________________________ ________________________________________________\n\n\nKonrad\nMüller\nImp erial\nSession 4\n\n\nFrancesco\nPiatti\nImperial\n\n\nMarco\nRodrigues\nE TH\n\n\nMateo\nRodriguez\nETH\n\n\n\n\n\n_________________________________ ________________________________________________________\n\n\nQinxin\nYan\ nETH\nSession 5\n\n\nYun\nZhao\nImperial\n\n\nDaniel\nKrsek\nETH\n\n\nJose ph\nMulligan\nImperial\n\n\n\n\n \nTalk Information\nDohyun Ahn\nTitle:  Efficient Simulation of Polyhedral Expectations with Applications to Finan ce\nAbstract: We consider the problem of estimating the expectation over a convex polyhedron specified by a set of linear inequalities. This problem encompasses a multitude of financial applications including systemic risk quantification\, exotic option pricing\, and portfolio management. We par ticularly focus on the case where the target event is rare\, which corresp onds to extreme systemic failures\, deep out-of-the-money options\, and hi gh target returns in the aforementioned applications\, respectively. This rare-event setting renders the naive Monte Carlo method inefficient and re quires the use of variance reduction techniques. To address this issue\, w e develop a novel and strongly efficient method for the computation of the said expectation in a general rare-event setting by exploiting the geomet ry of the target polyhedron and concentrating the sampling density almost within the polyhedron. The proposed method significantly outperforms the e xisting approaches in various numerical experiments in terms of accuracy a nd computational costs.\nRobert Boyce\nTitle: Unwinding Stochastic Order F low with Partial Information\nAbstract: We consider the problem faced by a trader who wishes to unwind a stochastic order flow with uncertainty on t he model parameterisation. Specifically\, the order flow in this model is a stochastic process and it is influenced by unknown\, intraday\, low-freq uency toxicity which reacts to the trader’s unwind strategy. As a result \, the trader’s problem is an optimal liquidation problem\, where the am ount to liquidate is stochastic and evolves\, and the adversarial effect o f the order flow toxicity is unknown.\nKexin Chen\nTitle: Robust Dividend Policy: Equivalence of Epstein-Zin and Maenhout Preferences\nAbstract: The classic optimal dividend problem aims to maximize the expected discounted dividend stream over the lifetime of a company. Since dividend payments a re irreversible\, this problem corresponds to a singular control problem w ith a risk-neutral utility function applied to the discounted dividend str eam. In cases where the company’s surplus process encounters model ambig uity under the Brownian filtration\, we explore robust dividend payment st rategies in worst-case scenarios. We establish a connection between ambigu ity aversion in a robust singular control problem and risk aversion in Eps tein-Zin preferences. To do so\, we first formulate the dividend problem a s a recursive utility function with the EZ aggregator within a singular co ntrol framework. We investigate the existence and uniqueness of the EZ div idend problem. By employing Backward Stochastic Differential Equation (BSD E) representations where singular controls are involved in the generators of BSDEs\, we demonstrate that the EZ formulation is equivalent to the max imin problem involving risk-neutral utility on the discounted dividend str eam\, incorporating Meanhout’s regularity that reflects investors’ amb iguity aversion. Considering the equivalent Meanhout’s preferences\, we solve the robust dividend problem using a Hamilton-Jacobi-Bellman (HJB) ap proach combined with a variational inequality (VI). Our solution is obtain ed through a novel shooting method that simultaneously satisfies the VI an d boundary conditions. This is a joint work with Kyunghyun Park and Hoi Yi ng Wong.\nNan Chen\nTitle: A Two Timescale Evolutionary Game Approach to M ulti-Agent Reinforcement Learning and its Application in Algorithmic Collu sion.\nAbstract: In this paper\, we propose a novel two timescale evolutio nary game approach for solving general-sum multi-agent reinforcement learn ing (MARL) problems. Unlike existing literature that requires solving Nash equilibrium exactly or approximately in each learning episode\, our new a pproach combines three key design components. First\, we introduce a simpl e perturbed best response-based protocol for policy updates\, avoiding the computationally expensive task of finding exact equilibria at each state. Second\, agents use fictitious play to update their beliefs about other a gents’ policies\, relaxing the requirement for observable Q-values of al l agents as in classical Nash Q-learning. Third\, our algorithm updates po licies\, beliefs\, and Q-values at two different time scales to address no n-stationarity during learning. Importantly\, our approach converges to ap proximate Nash equilibria for MARL problems without relying on global opti mality or saddle point conditions\, which are typically restrictive assump tions in the literature.\nAdditionally\, AI-powered algorithms are increas ingly used in marketplaces for pricing goods and services. However\, regul ators and academia express concerns about the potential collusion among th ese algorithms during strategic interactions. Most researchers rely on Q-l earning to model pricing algorithm behavior\, but this lacks convergence g uarantees. Our approach provides a novel framework for algorithmic collusi on studies.\nThis is a joint work with Ruixun Zhang and Yumin Xu (Peking U niversity) and Mingyue Zhong (Tsinghua University).\nRobert Crowell\nTitle : McKean—Vlaosv SDEs: New results on existence of weak solutions and on propagation of chaos\n\nAbstract: We consider weak solutions of McKean- ​Vlasov SDEs with common noise. We discuss the main steps to prove weak existence and identify more nuanced assumptions under which chaos propagat es. The results are obtained through a marriage of probabilistic and analy tic techniques for general non-​linear but uniformly elliptic coefficien ts that posses only low spatial regularity.\n\nShuoqing Deng\nTitle: Stabi lity of SMOT and the associated monotonicity principle.\nAbstract: In this work\, we shall study the stability of the supermartingale optimal transp ort(SMOT) problem. First\, we consider the (lifted) canonical SMOT plans\, and establish in particular the stability of the supermartingale shadow m easures. Then\, we shall focus on the more general SMOT problem\, and esta blish the stability of the primal value and the transport plan. As a bi-pr oduct\, we shall also study a supermartingale version of C-monotonicity pr inciple for the Weak SMOT.\nBased on joint works with Erhan Bayraktar(Mich igan)\, Gaoyue Guo(CentraleSupelec) and Dominykas Norgilas(North Carolina State).\nIoannis Gasteratos\nTitle: Kolmogorov equations for Volterra proc esses\nAbstract: We study a class of Stochastic Volterra Equations (SVEs) with multiplicative noise and convolution-type kernels. Our focus lies on rough volatility models and thus we allow for kernels that are singular at the origin. Working with carefully chosen Hilbert spaces\, we rigorously establish a link between the solution of the SVE and the Markovian mild so lution of an associated Stochastic Partial Differential Equation (SPDE). O ur choice of a Hilbert space solution theory allows access to well-develop ed tools from stochastic calculus in infinite dimensions. In particular\, we obtain an Itˆo formula for functionals of the solution to the SPDE and show that its law and (conditional) expectations solve infinite-dimension al Fokker-Planck and backward Kolmogorov equations respectively. Time perm itting\, we shall discuss potential applications of our results to optimal control and long-time behaviour of SVEs. This is joint work with Alexandr e Pannier (Universit´e Paris Cit´e).\nLukas Gonon\nTitle: Quantum neural network expressivity\nAbstract: Quantum neural networks have recently em erged as novel machine learning tools\, suitable for implementations on qu antum hardware. In this talk we present results on quantum neural network expressivity. We provide a link between required circuit complexity and de sired approximation accuracy for functions with integrable Fourier transfo rm. As an application example we consider option pricing in exponential L évy models.\nThe talk is based on joint work with Antoine Jacquier.\nGuan gyi He\nTitle: Optimization of Portfolio Strategies Under Nonlinear Price Impact\n\nAbstract: In optimizing portfolio strategies under price impact\ , if the impact is linear\, there exists closed-form linear strategies. Ho wever\, the problem becomes significantly more complex with nonlinear pric e impact. This presentation introduces methods to approximate linear strat egies through linear approximation and demonstrates the use of neural netw orks to find optimal strategies.\n\nXuedong He\n\n\nTitle: Reference-depen dent asset pricing with a stochastic consumption-dividend ratio\nAbstract: We study a discrete-time consumption-based capital asset pricing model un der expectations-based reference-dependent preferences. More precisely\, w e consider an endowment economy populated by a representative agent who de rives utility from current consumption and from gains and losses in consum ption with respect to a forward-looking\, stochastic reference point. Firs t\, we consider a general model in which the agent’s preferences include both contemporaneous gain-loss utility\, that is\, utility from the diffe rence between current consumption and previously held expectations about c urrent consumption\, and prospective gain-loss utility\, that is\, utility from the difference between intertemporal beliefs about future consumptio n. A semi-closed form solution for equilibrium asset prices is derived for this case. We then specialize to a model in which the agent derives conte mporaneous gain-loss utility only\, obtaining equilibrium asset prices in closed from. Extensive numerical experiments show that\, with reasonable v alues of risk aversion and loss aversion\, our models can generate equity premia that match empirical estimates. Interestingly\, the models turn out to be consistent with some well-known empirical facts\, namely procyclica l variation in the price-dividend ratio and countercyclical variation in t he conditional expected equity premium and in the conditional volatility o f the equity premium. Furthermore\, we find that prospective gain-loss uti lity is necessary for the model to predict reasonable values of the price- dividend ratio.\n\n\nThis is a joint work with Luca De Gennaro Aquino\, Mo ris S. Strub\, and Yuting Yang\n\nSongyan Hou\nTitle: Time-Causal Market G enerator\n\n\nAbstract: The generation of synthetic data that mimics real- world observations is important across numerous fields\, in particular in finance due to the scarcity of data. While traditional metrics such as Was serstein distances are prevalentforassessing distribution similarity\, fin ancial applications demand stronger metrics like causal or adapted Wassers tein distances\, as they provide Lipschitz robustnessforpricing\, hedging\ , and utility maximization problems under model uncertainty. Therefore\, t he generated paths are wished to be close to the data paths under causal o r adapted Wasserstein distance.\n\nWe introduce a novel solution: the time -causal variational autoencoder (TC-VAE) designed specificallyforcausal ro bustness. TC-VAE ensures that the causal Wasserstein distance between the data paths and the generated paths is controlled by our loss objective fun ction. Through extensive experimentation on synthetic and market data\, we showcase TC-VAE’s generative prowess and its generation robustness to s tochastic optimization challenges. In essence\, TC-VAE represents a promis ing avenueforsynthetic financial data generation with robustness guarantee of stochastic optimization problems.\n\nThis is joint work with Beatrice Acciaio and Stephan Eckstein\n\n\nDavid Itkin\nTitle: Rank-based volatili ty stabilized models for equity markets.\n \nAbstract: In the framework o f stochastic portfolio theory\, we introduce rank volatility stabilized mo dels for large equity markets over long time horizons. These models are ra nk-based extensions of the volatility stabilized models introduced by Fern holz & Karatzas\, which are known to admit relative arbitrage. On the theo retical side we establish global existence of the model and ergodicity of the induced ranked market weights. On the empirical side we calibrate the model to sixteen years of CRSP US equity data matching (i) rank-based vola tilities\, (ii) stock turnover as measured by market weight collisions\, ( iii) the average market rate of return and (iv) the capital distribution c urve. To the best of our knowledge this is the first model exhibiting rela tive arbitrage that has statistically been shown to have a good quantitati ve fit with the empirically estimable features (i)-(iv). We also simulate trajectories of the calibrated model and compare them to historical trajec tories\, both in and out of sample. This is based on joint work with Marti n Larsson.\n\n\n\nAntoine (Jack) Jacquier\nTitle: Wondering about the link between Optimal Transport and Quantum Adiabatic Theorem. Any help appreci ated!\nYanwei Jia \nTitle: Continuous-time Risk-sensitive Reinforcement L earning via Quadratic Variation Penalty\nAbstract: This paper studies cont inuous-time risk-sensitive reinforcement learning (RL) under the entropy-r egularized\, exploratory diffusion process formulation with the exponentia l form objective. The risk-sensitive objective arises either as the agent ’s risk attitude or as a distributionally robust approach against the mo del uncertainty. Owing to the martingale perspective in Jia and Zhou (2023 )\, the risk-sensitive RL problem is shown to be equivalent to ensuring th e martingale property of a process involving both the value function and t he q-function\, augmented by an additional penalty term: the quadratic var iation of the value process\, capturing the variability of the value-to-go along the trajectory. This characterization allows for the straightforwar d adaptation of existing RL algorithms developed for non-risk-sensitive sc enarios to incorporate risk sensitivity by adding the realized variance of the value process. Additionally\, I highlight that the conventional polic y gradient representation is inadequate for risk-sensitive problems due to the nonlinear nature of quadratic variation\; however\, q-learning offers a solution and extends to infinite horizon settings. Finally\, I prove th e convergence of the proposed algorithm for Merton’s investment problem and quantify the impact of temperature parameter on the behavior of the le arning procedure. I also conduct simulation experiments to demonstrate how risk-sensitive RL improves the finite sample performance in the linear-qu adratic control problem.\n\nZhaoli Jiang\nTitle: Strategic Investment unde r Uncertainty with First- and Second-mover Advantages \n\nAbstract: We an alyze firm entry in a duopoly real-option game. The interaction between f irst- and second-mover advantages gives rise to a unique Markov subgame-pe rfect symmetric equilibrium\, featuring state-contingent pure and mixed st rategies in multiple endogenously-determined regions. In addition to the s tandard option-value-of-waiting region\, a second waiting region arises be cause of the second-mover advantage. For sufficiently high market demand\, waiting preserves the second-mover advantage but forgoes profits. Two dis connected mixed-strategy regions where firms enter probabilistically surfa ce. In one such region\, Leader earns monopoly rents while Follower optima lly waits. Finally\, when the first-mover advantage dominates the second-m over advantage\, firms enter using pure strategies.\n\n\nFlorian Krach\nT itle: Path-Dependent Neural Jump ODEs and their forecasting capabilities i n LOBs\n\n\nAbstract: In this talk we study the problem of (online) foreca sting general stochastic processes using a path-dependent (PD) extension o f the Neural Jump ODE (NJ-ODE) framework. While NJ-ODE was the first frame work to establish convergence guarantees for the prediction of irregularly observed time series\, these results were limited to data stemming from I t\\^o-diffusions with complete observations\, in particular Markov process es\, where all coordinates are observed simultaneously. In this work\, we generalise these results to generic\, possibly non-Markovian or discontinu ous\, stochastic processes with incomplete observations\, by utilising the reconstruction properties of the signature transform. These theoretical r esults are supported by empirical studies. Applying the PD-NJ-ODE to the m idprice forecasting problem in limit order books\, once viewed as a regres sion and once as a classification problem\, leads to state-of-the-art resu lts. This is joint work with Marc Nübel and Josef Teichmann.\n\nDaniel Kr sek\nTitle: Randomisation with moral hazard: a path to existence of optima l contracts\nAbstract: We discuss recent advancements in contracting theor y. We consider a generic principal-agent problem in continuous time and in troduce a framework in which the agent chooses relaxed controls. We charac terize the agent’s value process as a solution to a BSDE driven by a mar tingale measure. This\, in turn\, allows us to employ compactification tec hniques and show the existence of optimal contracts\, even with very gener al constraints imposed on the contract. The talk is based on joint work wi th Dylan Possamaï.\nLingfei Li\nTitle: Model-based reinforcement learning in diffusion environments \nAbstract: We study continuous-time model-base d reinforcement learning where the environment is modelled by a stochastic differential equation that defines a diffusion process. Instead of estima ting the diffusion model by a statistical method such as maximum likelihoo d estimation (MLE)\, we pursue a value-aware approach for model learning t hat takes the structure of the decision problem into account\, which has t he potential of finding a better model for policy learning than the classi cal statistical approach when model misspecification exists. To perform va lue-aware estimation\, we minimize the mismatch between the model-based va lue function and empirical rewards from the real environment and solve thi s problem based on numerically solving the value function partial differen tial equation. We develop a theory of our estimation approach. When the mo del is correctly specified\, we establish convergence and asymptotic prope rties using the machinery of generalized method of moments. In the general case where model misspecification can exist\, we obtain a representation that shows how the value function error is determined by the model error. We consider the problem of mean-variance portfolio selection to evaluate o ur method and demonstrate its advantages over model learning via MLE and t he model-free approach in an empirical study.\n\nTengyingzi Ma\nTitle: Rei nforcement learning in Microbial risk management\nAbstract: By applying co ncepts from financial mathematics to microbial risk management\, we work o n sustainable food systems. As the first project\, we combine Markov decis ion processes with observation costs to optimise food production chains.\n \nJohannes Muhle-Karbe\nTitle: Concave Cross Impact\nAbstract: The price i mpact of large orders is well known to be a concave function of trade size .\nWe discuss how to extend models consistent with this “square-root law ” to multivariate settings with\ncross impact\, where trading each asset also impacts the prices of the others. In this context\, we derive\nconsi stency conditions that rule out price manipulation\, discuss how cross imp act affects optimal\ntrading strategies\, and illustrate these results usi ng CFM metaorder data.\n(Joint work in progress with Natascha Hey and Iaco po Mastromatteo)\n\nJoseph Mulligan\nTitle: In-Sample and Out-of-Sample Sh arpe Ratios for Linear Prediction Models.\nAbstract: Before using a quanti tative trading strategy\, it should first be tested. This process has the potential to be fraught with issues which cause the in-sample performance to be significantly overestimated in relation to the out-of-sample perform ance of the strategy. We study the potential for overfitting when using a linear predictive model to trade and give analytical expressions for the i n-sample and out-of-sample expected return and variance. We also show how these findings relate to the existing literature on estimation errors in p ortfolio optimisation and multiple testing.\nEyal Neumann\nTitle: Equilibr ium in Functional Stochastic Games with Mean-Field Interaction\nAbstract: We model the interaction between a slow institutional investor and a high- frequency trader as a stochastic multiperiod Stackelberg game.\nThe high-f requency trader exploits price information more frequently and is subject to periodic inventory constraints.  We first derive the optimal strategy of the high-frequency trader given any admissible strategy of the institut ional investor. Then\, we solve the problem of the institutional investor given the optimal  strategy of the high-frequency trader\, in terms of th e resolvent of a Fredholm integral equation\, thus establishing the unique multi-period Stackelberg equilibrium of the game. Our results provide an explicit solution which shows that the high-frequency trader can adopt eit her predatory or cooperative strategies in each period\, depending on the tradeoff between the order-flow and the trading signal. We also show that the institutional investor’s strategy is more profitable when the order- flow of the high-frequency trader is taken into account.\nThis is a joint work with Eduardo Abi Jaber and Moritz Voss.\nMikko Pakkanen\nTitle: A G MM approach to estimate the roughness of stochastic volatility\nAbstract: I will present an approach to estimate log normal stochastic volatility m odels\, including rough volatility models\, using the generalised method o f moments (GMM). In this GMM approach\, estimation is done directly usin g realised measures (realised variance and the like)\, avoiding the biases that arise from treating the realised measures as proxies of spot volatil ity. I will also present asymptotic theory for the GMM estimator\, permi tting statistical inference\, and apply the methodology to Oxford-Man Real ised volatility data. Joint work with Anine Bolko\, Kim Christensen and Be zirgen Veliyev.\nDylan Possamaï\nTitle: A target approach to Stackelberg games.\n\nAbstract: In this paper\, we provide a general approach to refo rmulating any continuous-time stochastic Stackelberg differential game und er closed-loop strategies as a single-level optimisation problem with targ et constraints. More precisely\, we consider a Stackelberg game in which t he leader and the follower can both control the drift and the volatility o f a stochastic output process\, in order to maximise their respective expe cted utility. The aim is to characterise the Stackelberg equilibrium when the players adopt “closed-loop strategies”\, i.e. their decisions are based solely on the historical information of the output process\, excludi ng especially any direct dependence on the underlying driving noise\, ofte n unobservable in real-world applications. We first show that\, by conside ring the-second-order-backward stochastic differential equation associated with the continuation utility of the follower as a controlled state varia ble for the leader\, the latter’s unconventional optimisation problem can be reformulated as a more standard stochastic control problem with sto chastic target constraints. Thereafter\, adapting the methodology develope d by Soner and Touzi or Bouchard\, Élie\, and Imbert\, the optimal strate gies\, as well as the corresponding value of the Stackelberg equilibrium\, can be characterised through the solution of a well-specified system of H amilton–Jacobi–Bellman equations. For a more comprehensive insight\, we illustrate our approach through a simple example\, facilitating both t heoretical and numerical detailed comparisons with the solutions under dif ferent information structures studied in the literature. This is a joint w ork with Camilo Hernández\, Nicolás Hernández Santibáñez\, and Emma H ubert.\n\nMarco Rodrigues\nTitle: Reflections on BSDEs.\nAbstract: We cons ider backward stochastic differential equations (BSDEs) and reflected BSDE s in a generality that allows for a unified study of certain discrete-ti me and continuous-time control problems with random time horizons. We prov ide well-posedness results for BSDEs and reflected BSDEs with optional o bstacle processes\, given appropriately weighted square-integrable data\, and touch upon the corresponding second-order BSDEs. This is based on join t work with Dylan Possamaï.\nYonatan Shadmi\nTitle: Stability of order Ro uting Systems in Fragmented Markets.\n\nAbstract: We study an order rout ing system with multiple limit order book exchanges proposed by Maglaras e t al. (2021). In this model traders of different types choose where to pla ce their limit orders according to a trade-off between expected execution time and trading fees\, and place their market orders by prioritizing exch anges with more liquidity. We rigorously prove convergence to the fluid li mit of this queueing routing system and characterise it as a system of cou pled nonlinear ODEs. Then we prove local asymptotic stability\, as well as global asymptotic stability for the fluid limit for any number of exchang es N ≥ 2 in the case where they are equality weighted\, hence extending the stability results for two exchanges system by Maglaras et al.\n\nPietr o Siorpaes\nTitle: A computable quantisation of measures which preserves t he convex order\nAbstract: We consider an optimal transport problem with l inear constraints (P). When the marginals are finitely supported\, (P) is a linear program\, and thus is well understood and can be solved numerical ly with high efficiency. It is then of interest to approximate the general marginals with some finitely supported ones which satisfy the same linear constraints\, are such that the optimal values of the corresponding probl em (P) converge. We do this for the martingale transport problem\, whose o ptimal value provides robust upper and lower bounds for derivatives’ pri ces. In this case\, the constraint specifies that the marginals have to be increasing in convex order. Thus\, we construct a quantisation method whi ch preserves the convex order (in any dimension)\, and compare our results with the several methods found in the literature. We show how our method can be applied concretely when the marginals belong to some common familie s of probabilities (e.g. stable and log-stable laws).\nThis is joint work with Marco Massa.\n\nJosef Teichmann\nTitle: Path dependence in Finance an d Computer Science\n\nAbstract: We analyze from a mathematical perspective the advantage of modelling dynamic phenomena on given state spaces by pat h dependent rather than state dependent characteristics. This is suggested by recent modelling successes in Finance or language generation.\nSturmiu s Tuschmann\nTitle: Optimal Portfolio Choice with Cross-Impact\n\nAbstract : Cross-impact describes the phenomenon where trades for one asset impact the price of another asset. We study cross-impact from a theoretical persp ective\, by considering an optimal portfolio choice problem in which the a gent seeks to maximise a revenue-risk functional in the presence of linear transient cross-impact driven by a matrix-valued propagator and temporary price impact. We solve the maximisation problem explicitly by reducing it to a coupled system of stochastic Fredholm equations and deriving its sol ution. We then discuss the influence of cross-impact on the optimal strate gies and its interplay with alpha decays.\n\nChen Yang\nTitle: Optimal Tax -Timing with Transaction Costs\nAbstract: We develop a dynamic portfolio m odel incorporating capital gains tax (CGT)\, financial transaction tax\, a nd transaction costs\, where the tax amount is calculated at the end of ea ch year. We find that transaction costs affect loss deferrals much more th an gain deferrals\, and a lower interest rate makes higher-wealth investor s realize losses sooner but makes lower-wealth ones realize losses later. Our model can help explain the puzzle that even when investors face equal long-term/short-term CGT rates or almost zero interest rates\, they may st ill defer realizing large capital losses. In addition\, it provides severa l unique\, empirically testable predictions and can shed light on recently proposed tax policy changes. This talk is based on a joint work with Min Dai\, Yaoting Lei\, and Hong Liu.\n\n\n\nYufei Zhang\n\nTitle: Alpha poten tial games: A new paradigm for N-player gamesAbstract: Static potential ga mes\, pioneered by Monderer and Shapley (1996)\, are non-cooperative games in which there exists an auxiliary function called static potential funct ion\, so that any player’s change in utility function upon unilaterally deviating from her policy can be evaluated through the change in the value of this potential function. The introduction of the potential function is powerful as it simplifies the otherwise challenging task of finding Nash equilibria for non-cooperative games: maximizers of potential functions le ad to the game’s Nash equilibria. In this talk\, we propose an analogou s and new framework called $\\alpha$-potential game for dynamic $N$-player games\, with the potential function in the static setting replaced by an $\\alpha$-potential function. We present an analytical characterization of $\\alpha$-potential functions for any dynamic game. For stochastic differ ential games in which the state dynamic is a controlled diffusion\, $\\alp ha$ is explicitly identified in terms of the number of players\, the choic e of admissible strategies\, and the intensity of interactions and the lev el of heterogeneity among players. We provide detailed analysis for games with mean-field interactions\, distributed games\, and crowd aversion gam es\, for which $\\alpha$ is shown to decay to zero as the number of player s goes to infinity\, even with heterogeneity in state dynamics\, cost func tions\, and admissible strategy classes. We also show $\\alpha$ is capable of capturing the subtle difference between the open-loop and closed-loop strategies.The talk is based on joint work with Xin Guo and Xinyu Li: http s://arxiv.org/abs/2403.16962  URL:https://www.imperial.ac.uk/events/170432/first-edition-of-the-london-zu rich-and-hong-kong-mathematical-finance-workshop/ DTSTART;TZID=Europe/London:20240617T090000 DTEND;TZID=Europe/London:20240620T163000 LOCATION:340\, Huxley Building\, South Kensington Campus\, Imperial College London\, London\, SW7 2AZ\, United Kingdom END:VEVENT BEGIN:VTIMEZONE TZID:Europe/London BEGIN:DAYLIGHT DTSTART:20240617T090000 TZNAME:BST TZOFFSETTO:+0100 TZOFFSETFROM:+0100 END:DAYLIGHT END:VTIMEZONE END:VCALENDAR