## Publications

31 results found

Muhle-Karbe J, Wang Z, Webster K, 2022, A Leland Model for Delta Hedging in Central Risk Books

Micheli A, Muhle-Karbe J, Neuman E, 2021, Closed-Loop Nash Competition for Liquidity

Herdegen M, Muhle-Karbe J, Stebegg F, 2021, Liquidity Provision with Adverse Selection and Inventory Costs

Gonon L, Muhle-Karbe J, Shi X, 2021, Asset pricing with general transaction costs: Theory and numerics, *Mathematical Finance*, Vol: 31, Pages: 595-648, ISSN: 0960-1627

We study risk-sharing equilibria with general convex costs on the agents' trading rates. For an infinite-horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean-revert around their frictionless counterparts—the deviation has Ornstein-Uhlenbeck dynamics for quadratic costs whereas it follows a doubly-reflected Brownian motion if costs are proportional. More general models with arbitrary state dynamics and endogenous volatilities lead to multidimensional systems of nonlinear, fully-coupled forward-backward SDEs. These fall outside the scope of known well-posedness results, but can be solved numerically using the simulation-based deep-learning approach of Han, Jentzen, and E (2018). In a calibration to time series of prices and trading volume, realistic liquidity premia are accompanied by a moderate increase in volatility. The effects of different cost specifications are rather similar, justifying the use of quadratic costs as a proxy for other less tractable specifications.

Muhle-Karbe J, Shi X, Yang C, 2020, An Equilibrium Model for the Cross-Section of Liquidity Premia

MuhleKarbe J, Nutz M, Tan X, 2020, Asset pricing with heterogeneous beliefs and illiquidity, *Mathematical Finance*, Vol: 30, Pages: 1392-1421, ISSN: 0960-1627

Herdegen M, Muhle-Karbe J, Possamaï D, 2020, Equilibrium Asset Pricing with Transaction Costs

Cayé T, Herdegen M, Muhle-Karbe J, 2020, Trading with small nonlinear price impact, *Annals of Applied Probability*, Vol: 30, Pages: 706-746, ISSN: 1050-5164

We study portfolio choice with small nonlinear price impact on general market dynamics. Using probabilistic techniques and convex duality, we show that the asymptotic optimum can be described explicitly up to the solution of a nonlinear ODE, which identifies the optimal trading speed and the performance loss due to the trading friction. Previous asymptotic results for proportional and quadratic trading costs are obtained as limiting cases. As an illustration, we discuss how nonlinear trading costs affect the pricing and hedging of derivative securities and active portfolio management.

Muhle-Karbe J, Nutz M, Tan X, 2020, Asset Pricing with Heterogeneous Beliefs and Illiquidity

Herrmann S, Muhle-Karbe J, Shang D,
et al., 2020, Inventory Management for High-Frequency Trading with Imperfect Competition, *SIAM JOURNAL ON FINANCIAL MATHEMATICS*, Vol: 11, Pages: 1-26, ISSN: 1945-497X

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Guasoni P, Liu R, Muhle-Karbe J, 2019, Who should sell stocks?, *Mathematical Finance*, Vol: 29, Pages: 448-482, ISSN: 0960-1627

Cohen SN, Henckel T, Menzies GD,
et al., 2018, Switching Cost Models as Hypothesis Tests, *Economics Letters*, ISSN: 0165-1765

Ekren I, Muhle-Karbe J, 2018, Portfolio Choice with Small Temporary and Transient Price Impact, *Mathematical Finance*, ISSN: 0960-1627

Belak C, Muhle-Karbe J, Ou K, 2018, Optimal Trading with General Signals and Liquidation in Target Zone Models

Bank P, Ekren I, Muhle-Karbe J, 2018, Liquidity in competitive dealer markets

We study a continuous-time version of the intermediation model of Grossman and Miller (1988). To wit, we solve for the competitive equilibrium prices at which liquidity takers' demands are absorbed by dealers with quadratic inventory costs, who can in turn gradually transfer these positions to an end-user market. This endogenously leads to a model with transient price impact. Smooth, diffusive, and discrete trades all incur finite but nontrivial liquidity costs, and can arise naturally from the liquidity takers' optimization.

Bouchard B, Fukasawa M, Herdegen M,
et al., 2018, Equilibrium Returns with Transaction Costs, *Finance and Stochastics*, Pages: 569-601, ISSN: 1432-1122

Herdegen M, Muhle-Karbe J, 2018, Stability of Radner equilibria with respect to small frictions, *Finance and Stochastics*, Vol: 22, Pages: 443-502, ISSN: 0949-2984

We study risk-sharing equilibria with trading subject to small proportional transaction costs. We show that the frictionless equilibrium prices also form an “asymptotic equilibrium” in the small-cost limit. More precisely, there exist asymptotically optimal policies for all agents and a split of the trading cost according to their risk aversions for which the frictionless equilibrium prices still clear the market. Starting from a frictionless equilibrium, this allows studying the interplay of volatility, liquidity and trading volume.

Muhle-Karbe J, Nutz M, 2018, A risk-neutral equilibrium leading to uncertain volatility pricing, *Finance and Stochastics*, Vol: 22, Pages: 281-295, ISSN: 0949-2984

Muhle-Karbe J, Reppen M, Soner HM, 2017, A Primer on Portfolio Choice with Small Transaction Costs, *Annual Review of Financial Economics*, Vol: 9, Pages: 301-331

Herrmann S, Muhle-Karbe J, 2017, Model uncertainty, recalibration, and the emergence of delta–vega hedging, *Finance and Stochastics*, Vol: 21, Pages: 873-930, ISSN: 0949-2984

Muhle-Karbe J, Webster K, 2017, Information and Inventories in High-Frequency Trading

Ekren I, Liu R, Muhle-Karbe J, 2017, Optimal Rebalancing Frequencies for Multidimensional Portfolios

Moreau L, Muhle-Karbe J, Soner HM, 2017, Trading with Small Price Impact, *Mathematical Finance*, Vol: 27, Pages: 350-400, ISSN: 0960-1627

Guasoni P, Muhle-Karbe J, Xing H, 2017, ROBUST PORTFOLIOS AND WEAK INCENTIVES IN LONG-RUN INVESTMENTS, *Mathematical Finance*, Vol: 27, Pages: 3-37, ISSN: 0960-1627

Guasoni P, Muhle-Karbe J, 2015, LONG HORIZONS, HIGH RISK AVERSION, AND ENDOGENOUS SPREADS, *Mathematical Finance*, Vol: 25, Pages: 724-753, ISSN: 0960-1627

Guasoni P, Muhle-Karbe J, Xing H, 2013, Robust Portfolios and Weak Incentives in Long Run Investments, *Boston U. School of Management Research Paper*

Gerhold S, Guasoni P, Muhle-Karbe J,
et al., 2013, Transaction Costs, Trading Volume, and the Liquidity Premium, *Boston U. School of Management Research Paper*

Guasoni P, Muhle-Karbe J, 2012, Portfolio Choice with Transaction Costs: A User's Guide, *Boston U. School of Management Research Paper*

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