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 un...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.展开更多
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 infor...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.展开更多
基金supported by the National Natural Science Foundation of China(11571388)the MOE Project of Key Research Institute of Humanities and Social Sciences at Universities(15JJD790036)+2 种基金the 111 Project(B17050)supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.HKU17329216)supported by the National Natural Science Foundation of China(11571198,11701319)
文摘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.
基金Supported by the Program for New Century Excellent Talents in University(NCET)the National Key Basic Research and Devel-opment (973) Program of China(No. 2007CB814902)the National Natural Science Foundation of China(Nos. 70671067 and71071086)
文摘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.
