Optimality Studies for Contemporary Insurance Models

Professor Yuen, Kam Chuen   (Principal Investigator (PI))

48

2017-01-01

488501

Optimality Studies for Contemporary Insurance Models

Capital injection, Dividend, Model uncertainty, Regime switching, Reinsurance

Mathematical Finance and Insurance,Applied Mathematics

Physical Sciences (P)

17329216

General Research Fund (GRF)

2016

Completed

1 The first objective is to investigate the optimal capital injection, dividends and reinsurance for a risk model with the thinning dependence. Under non-cheap reinsurance and variance reinsurance premium principle, the proposed problem of study becomes more interesting but challenging. In the presence of capital injection, one can consider two suboptimal problems when the surplus goes below zero: (i) capital injection must take place; and (ii) capital injection is not a must, and hence bankruptcy is allowed. For both bounded dividend rate and unbounded dividend rates, our goal is to derive optimal results that maximize the expected discounted dividend payments minus the discounted costs of capital injection. 2 The second objective is to study the optimal investment and reinsurance problem in a financial market with a jump-diffusion risky asset, where the insurance risk model is modulated by a compound Poisson process. The investment and insurance jump-number processes are correlated through a common shock, and the expected value of the jump size in the risky asset can be negative. The idea of making the investment and insurance processes dependent in the optimal control problem is not only new but also practically sensible especially when some human or natural disasters cause a period of economic adversity. Our plan is to derive optimal investment and reinsurance strategies under the criterion of maximizing the expected the expected exponential utility. 3 The third project objective is to examine the optimal investment and reinsurance problem with common shock dependence in a regime-switching financial market under the mean-variance criterion. Here the market modes are divided into a finite number of regimes, and the nonnegative constraint of the investment-reinsurance policies are considered. These indeed introduce some technical difficulties since the optimal strategies derived in the usual way may not meet the restriction. It is hoped that the problem can be fixed by adding some conditions on the initial amount of wealth. Within this framework, our aim is to derive closed-form expressions for the mean-variance efficient strategies and efficient frontiers by using the techniques of stochastic linear-quadratic control.