Publications
72 results found
Bian B, Wu N, Zheng H, 2016, Optimal liquidation in a finite time regime switching model with permanent and temporary pricing impact, Discrete and Continuous Dynamical Systems - Series B, Vol: 21, Pages: 1401-1420, ISSN: 1553-524X
In this paper we discuss the optimal liquidation over a finite time horizon until the exit time. The drift and diffusion terms of the asset price are general functions depending on all variables including control and market regime. There is also a local nonlinear transaction cost associated to the liquidation. The model deals with both the permanent impact and the temporary impact in a regime switching framework. The problem can be solved with the dynamic programming principle. The optimal value function is the unique continuous viscosity solution to the HJB equation and can be computed with the finite difference method.
Liu C, Zheng H, 2015, Asymptotic analysis for target asset portfolio allocation with small transaction costs, Insurance Mathematics & Economics, Vol: 66, Pages: 59-68, ISSN: 0167-6687
In this paper we discuss the asset allocation in the presence of small proportional transaction costs. The objective is to keep the asset portfolio close to a target portfolio and at the same time to reduce the trading cost in doing so. We derive the variational inequality and prove a verification theorem. Furthermore, we apply the second order asymptotic expansion method to characterize explicitly the optimal no transaction region when the transaction cost is small and show that the boundary points are asymmetric in relation to the target portfolio position, in contrast to the symmetric relation when only the first order asymptotic expansion method is used, and the leading order is a constant proportion of the cubic root of the small transaction cost. In addition, we use the asymptotic results for the boundary points and obtain an expansion for the value function. The results are illustrated in the numerical example.
Ma J, Deng D, Zheng H, 2015, Convergence analysis and optimal strike choice for static hedges of general path-independent pay-offs, Quantitative Finance, Vol: 16, Pages: 593-603, ISSN: 1469-7696
In this paper, we propose a new algorithm to find the optimal static replicating portfolios for general path-independent nonlinear pay-off functions and give an estimate for the rate of convergence that is absent in the literature. We choose the static replication by designing an adaptation function arising in the error bound between the nonlinear pay-off function and the linear spline approximation and derive the equidistribution equation for selecting the optimal strikes. The numerical tests for variance swaps, swaptions, static quadratic hedges and also for a jump-diffusion process, allowing for the default of the underlying asset, show that the proposed iterative equidistribution equation algorithm is simple, fast and accurate. The paper generalizes and improves the results on static replication and approximation in the literature.
Westray N, Zheng H, 2015, CONSTRAINED NONSMOOTH UTILITY MAXIMIZATION ON THE POSITIVE REAL LINE, Publisher: AMER INST MATHEMATICAL SCIENCES-AIMS
Bian B, Hu S, Yuan Q, et al., 2015, Constrained viscosity solution to the HJB equation arising in perpetual American employee stock options pricing, Discrete and Continuous Dynamical Systems, Vol: 35, Pages: 5413-5433, ISSN: 1553-5231
Dong X, Zheng H, 2015, Intensity process for a pure jump Levy structural model with incomplete information, Stochastic Processes and Their Applications, Vol: 125, Pages: 1307-1322, ISSN: 0304-4149
Li Y, Zheng H, 2015, Weak Necessary and Sufficient Stochastic Maximum Principle for Markovian Regime-Switching Diffusion Models, APPLIED MATHEMATICS AND OPTIMIZATION, Vol: 71, Pages: 39-77, ISSN: 0095-4616
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- Citations: 8
Gu J-W, Jiang B, Ching W-K, et al., 2014, On modeling economic default time: a reduced-form model approach, Computational Economics, Vol: 47, Pages: 157-177, ISSN: 1572-9974
In the aftermath of the global financial crisis, much attention has been paid to investigating the appropriateness of the current practice of default risk modeling in banking, finance and insurance industries. A recent empirical study by Guo et al. (Rev Deriv Res 11(3): 171–204, 2008) shows that the time difference between the economic and recorded default dates has a significant impact on recovery rate estimates. Guo et al. (http://arxiv.org/abs/1012.0843, 2011) develop a theoretical structural firm asset value model for a firm default process that embeds the distinction of these two default times. In this paper, we assume the market participants cannot observe the firm asset value directly and we develop reduced-form models for characterizing the economic and recorded default times. We derive the probability distributions of these two default times. Numerical experiments with empirical data are given to demonstrate the proposed models. Our approach helps researchers to gain a new perspective for economic and recorded defaults and is more feasible in general practice compared with current method. Our results can also contribute to the understanding of the impacts of various parameters on the economic and recorded default times.
Bian B, Zheng H, 2014, Turnpike property and convergence rate for an investment model with general utility functions, Journal of Economic Dynamics & Control, Vol: 51, Pages: 28-49, ISSN: 0165-1889
Gu J-W, Ching W-K, Siu T-K, et al., 2014, On reduced-form intensity-based model with 'trigger' events, JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY, Vol: 65, Pages: 331-339, ISSN: 0160-5682
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- Citations: 3
Zhu D-M, Xie Y, Ching W-K, et al., 2014, On Pricing and Hedging Basket Credit Derivatives with Dependent Structure, IEEE Conference on Computational Intelligence for Financial Engineering and Economics (CIFEr), Publisher: IEEE, Pages: 435-440, ISSN: 2380-8454
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- Citations: 1
Gu J-W, Ching W-KC, Zheng H, 2014, A Hidden Markov Reduced-form Risk Model, IEEE Conference on Computational Intelligence for Financial Engineering and Economics (CIFEr), Publisher: IEEE, Pages: 190-196, ISSN: 2380-8454
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- Citations: 2
Gu J-W, Ching W-K, Siu T-K, et al., 2013, On pricing basket credit default swaps, QUANTITATIVE FINANCE, Vol: 13, Pages: 1845-1854, ISSN: 1469-7688
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- Citations: 10
Zheng H, 2013, A la Carte of Correlation Models: Which One to Choose?, Publisher: Quantitative Finance
In this paper we propose a copula contagion mixture model for correlated default times. The model includes the well known factor, copula, and contagion models as its special cases. The key advantage of such a model is that we can study the interaction of different models and their pricing impact. Specifically, we model the marginal default times to follow some contagion intensity processes coupled with copula dependence structure. We apply the total hazard construction method to generate ordered default times and numerically compare the pricing impact of different models on basket CDSs and CDOs in the presence of exponential decay and counterparty risk.
Zheng H, 2013, Contagion models a la carte: which one to choose?, QUANTITATIVE FINANCE, Vol: 13, Pages: 399-405, ISSN: 1469-7688
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- Citations: 4
Gu JW, Ching WK, Siu TK, et al., 2013, On modeling credit defaults: a probabilistic boolean network approach, Risk and Decision Analysis, Vol: 4, Pages: 119-129
Westray N, Zheng H, 2011, Minimal sufficient conditions for a primal optimizer in nonsmooth utility maximization, FINANCE AND STOCHASTICS, Vol: 15, Pages: 501-512, ISSN: 0949-2984
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- Citations: 6
Czichowsky C, Westray N, Zheng H, 2011, Convergence in the semimartingale topology and constrained portfolios, SEMINAIRE DE PROBABILITES XLIII, Pages: 395-412, ISSN: 0075-8434
Bian B, Miao S, Zheng H, 2011, Smooth value functions for a class of nonsmooth utility maximization problems, SIAM Journal on Financial Mathematics, Vol: 2, Pages: 727-747
In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is continuous on the closure of its domain. The key idea is to work on the dual control problem and the dual HJB equation. We construct a smooth, strictly convex solution to the dual HJB equation and show that its conjugate function is a smooth, strictly concave solution to the primal HJB equation satisfying the terminal and boundary conditions.
Lin J, Liang G, Wu S, et al., 2011, The valuation of the basket CDSs in the primary-subsidiary model, ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH, Vol: 28, Pages: 213-238, ISSN: 0217-5959
Xu G, Zheng H, 2010, Basket options valuation for a local volatility jump-diffusion model with the asymptotic expansion method, INSURANCE MATHEMATICS & ECONOMICS, Vol: 47, Pages: 415-422, ISSN: 0167-6687
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- Citations: 13
Xu G, Zheng H, 2009, Approximate basket options valuation for a jump-diffusion model, INSURANCE MATHEMATICS & ECONOMICS, Vol: 45, Pages: 188-194, ISSN: 0167-6687
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- Citations: 15
Zheng H, Jiang L, 2009, Basket CDS pricing with interacting intensities, FINANCE AND STOCHASTICS, Vol: 13, Pages: 445-469, ISSN: 0949-2984
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- Citations: 27
Zheng H, 2009, Efficient frontier of utility and CVaR, MATHEMATICAL METHODS OF OPERATIONS RESEARCH, Vol: 70, Pages: 129-148, ISSN: 1432-2994
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- Citations: 7
Westray N, Zheng H, 2009, Constrained nonsmooth utility maximization without quadratic inf convolution, STOCHASTIC PROCESSES AND THEIR APPLICATIONS, Vol: 119, Pages: 1561-1579, ISSN: 0304-4149
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- Citations: 9
Zheng H, Shen Y, 2008, Jump liquidity risk and its impact on CVaR, Journal of Risk Finance, Vol: 9, Pages: 477-492, ISSN: 1526-5943
Purpose – The aim is to study jump liquidity risk and its impact on risk measures: value at risk (VaR) and conditional VaR (CVaR).Design/methodology/approach – The liquidity discount factor is modelled with mean revision jump diffusion processes and the liquidity risk is integrated in the framework of VaR and CVaR. Findings – The standard VaR, CVaR, and the liquidity adjusted VaR can seriously underestimate the potential loss over a short holding period for rare jump liquidity events. A better risk measure is the liquidity adjusted CVaR which gives a more realistic loss estimation in the presence of the liquidity risk. An efficient Monte Carlo method is also suggested to find approximate VaR and CVaR of all percentiles with one set of samples from the loss distribution, which applies to portfolios of securities as well as single securities. Originality/value – The paper offers plausible stochastic processes to model liquidity risk.
Zheng H, 2007, Macaulay Duration for Nonparallel Shifts, Annual of Operations Research, Vol: 151, Pages: 179-191
Zheng H, 2006, Efficient hybrid methods for portfolio credit derivatives, QUANTITATIVE FINANCE, Vol: 6, Pages: 349-357, ISSN: 1469-7688
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- Citations: 5
Zheng H, 2006, Interaction of credit and liquidity risks: modelling and valuation, JOURNAL OF BANKING & FINANCE, Vol: 30, Pages: 391-407, ISSN: 0378-4266
Vinter RB, Zheng H, 2003, Some finance problems solved with nonsmooth optimization techniques, JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, Vol: 119, Pages: 1-18, ISSN: 0022-3239
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- Citations: 3
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