Risk-sensitive investment in a finite-factor model

A new jump diffusion regime-switching model is introduced, which allows for linking jumps in asset prices with regime changes. We prove the existence and uniqueness of the solution to the risk-sensitive asset management criterion maximisation problem in this setting. We provide an ODE for the optimal value function, which may be efficiently solved numerically. Relevant probability measure changes are discussed in the appendix. The approach of Klebaner and Lipster (2014) is used to prove the martingale property of the relevant density processes.Comment: 23 pages, 1 figur

On the Separation of Estimation and Control in Risk-Sensitive Investment Problems under Incomplete Observation

A typical approach to tackle stochastic control problems with partial observation is to separate the control and estimation tasks. However, it is well known that this separation generally fails to deliver an actual optimal solution for risk-sensitive control problems. This paper investigates the separability of a general class of risk-sensitive investment management problems when a finite-dimensional filter exists. We show that the corresponding separated problem, where instead of the unobserved quantities, one considers their conditional filter distribution given the observations, is strictly equivalent to the original control problem. We widen the applicability of the so-called Modified Zakai Equation (MZE) for the study of the separated problem and prove that the MZE simplifies to a PDE in our approach. Furthermore, we derive criteria for separability. We do not solve the separated control problem but note that the existence of a finite-dimensional filter leads to a finite state space for the separated problem. Hence, the difficulty is equivalent to solving a complete observation risk-sensitive problem. Our results have implications for existing risk-sensitive investment management models with partial observations in that they establish their separability. Their implications for future research on new applications is mainly to provide conditions to ensure separability

Crash Prediction Using Fundamental Variables: Evidence from Mainland China

This article investigates how fundamental crash prediction models perform in mainland China’s fast-growing equity markets. We apply three families of fundamental models, price-to-earnings ratio, cyclically adjusted price-to-earnings ratio, and bond-stock earnings yield differential, to the Shanghai and Shenzhen stock indices. Our statistical analysis supports the dominant view that Chinese equity markets behave different from U.S. markets. We find that fundamental models are significant predictors of equity market crashes in China despite these differences. Finally, we show how to use these crash prediction models to improve active portfolio management

Jump-Diffusion Asset-Liability Management Via Risk-Sensitive Control

Abstract In this paper, we use risk-sensitive control methods to solve a jumpdiffusion Asset-Liability Management (ALM) problem. We show that the ALM problem admits a unique classical (C 1,2 ) solution under two different sets of assumptions

Risk-sensitive benchmarked asset management

This paper extends the risk-sensitive asset management theory developed by Bielecki and Pliska and by Kuroda and Nagai to the case where the investor's objective is to outperform an investment benchmark. The main result is a mutual fund theorem. Every investor following the same benchmark will take positions, in proportions dependent on his/her risk sensitivity coefficient, in two funds: the log-optimal portfolio and a second fund which adjusts for the correlation between the traded assets, the benchmark and the underlying valuation factors.Asset management, Risk-sensitive stochastic control, Outperformance, Dynamic programming, Benchmark, Kelly criterion,