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Optimal Investment and Premium Control in a Nonlinear Diffusion Model

Acta Mathematicae Applicatae Sinica 2017年第4期33卷 945-958页

作者： Ming ZHOU Kam Chuen YUEN Chuan-cun YIN China Institute for Actuarial Science Central University of Finance and Economics Department of Statistics and Actuarial Science the University of Hong Kong School of Statistics Qufu Normal University

This paper considers the optimal investment and premium control problem in a diffusion approxi- mation to a non-homogeneous compound Poisson process. In the nonlinear diffusion model, it is assumed that there is an unspecified monotone function describing the relationship between the safety loading of premium and the time-varying claim arrival rate. Hence, in addition to the investment control, the premium rate can be served as a control variable in the optimization problem. Specifically, the problem is investigated in two cases：（i） maximizing the expected utility of terminal wealth, and （ii） minimizing the probability of ruin respectively. In both cases, some properties of the value functions are derived, and closed-form expressions for the optimal policies and the value functions are obtained. The results show that the optimal investment policy and the optimal premium control policy are dependent on each other. Most interestingly, as an example, we show that the nonlinear diffusion model reduces to a diffusion model with a quadratic drift coefficient when the function associated with the premium rate and the claim arrival rate takes a special form. This example shows that the model of study represents a class of nonlinear stochastic control risk model.

关键词： cara utility dependent control policies Hamilton-Jacobi-Bellman (HJB) equation investment premium control

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Who Wants to Be Informed-Less Risk Aversion or More Risk Aversion?

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Tsinghua Science and Technology 2011年第1期16卷 69-73页

作者：高健张丽宏宋逢明 School of Economics and Management Tsinghua University

Information is an important issue in financial markets since information advantage leads to increased profits. This paper investigates whether those with less risk aversion or more risk aversion would like to be informed when there is private information which can be acquired for a certain cost. The cara utility function and normal return assumptions were used to get the closed form solution of the absolute risk aversion coefficient which is indifferent to whether a person wants to be informed, which shows that the less risk aversion investor would like to be informed. The results further show that in financial markets, those people with lower risk aversion （for instance, institutional investors） are more favorable to information and price discovery of risky assets, which is consistent with intuition as well as empirical studies.

关键词： cara utility information risk aversion informed trader

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