Subject: Optimal financing of a firm: a hybrid strategy
Lecturer: Meng Hui
This paper investigates an optimal investment of capital into a large company or institution, in the form of cash. We first bring forward the decision maker can choose the types of injection capital including regular injection and impulse injection. The decision maker has the option to decide the capital injection rate and capital injection time and amount of impulse injection. Both of them have proportional cost, and fixed costs are considered in each impulse capital injection. The purpose of the decision maker is to find a strategy to minimize the cost of cash investment, but the constraint of the strategy is that it must ensure the firm has a positive cash flow. Under this rules, we analyze the optimal hybrid financing strategy dependent on the model cost parameters and show the sensibilities of the parameters to the optimal strategy and value function. This is a joint work with Ming Zhou and Peng Li.
Subject: On the optimality of deductibles with heterogeneous beliefs
Lecturer: Chi Yi Chun
It is known from Arrow's theorem that a risk averse insured, who wants to maximize the expected utility of its final wealth, will choose a deductible insurance policy when the insurance premium depends only upon the actuarial value of the coverage. It is noteworthy that Arrow's result is based on the assumption of the same probabilistic belief about the underlying loss for the insured and the insurer. Unfortunately, in insurance practice this assumption seldom holds true and both parties usually have different subjective beliefs because they possess asymmetric information. This talk attempts to extend Arrow's theorem of the deductible to the case of belief heterogeneity, and restricts the insurance contracts to be incentive-compatible for excluding ex post moral hazard. Specifically, both parties are asked to pay more for a larger realization of the loss, just like Huberman et al. (1983). It is shown that, ceteris paribus, the deductible insurance is optimal for any risk averse insured if and only if the insurer is more optimistic about the conditional loss given non-zero loss than the insured in the sense of monotone hazard rate order. This result can partly explain the popularity of deductible insurance in the market where the insurer with the diversification benefit and subject matter expertise is relatively optimistic. Finally, we derive the optimal deductible level explicitly for expected value premium principle, and investigate how it is affected by the changes of the insured's risk aversion, the insurance price and the belief heterogeneity.
Subject: Portfolio Selection by Minimizing the Present Value of Capital Injection Costs
Lecturer: Zhou Ming
This paper considers the portfolio selection and capital injection problem for a diffusion risk model within the classical Black–Scholes financial market. It is assumed that the original surplus process of an insurance portfolio is described by a drifted Brownian motion, and that the surplus can be invested in a risky asset and a risk-free asset. When the surplus hits zero, the company can inject capital to keep the surplus positive. In addition, it is assumed that both fixed and proportional costs are incurred upon each capital injection. Our objective is to minimize the expected value of the discounted capital injection costs by controlling the investment policy and the capital injection policy. We first prove the continuity of the value function and a verification theorem for the corresponding Hamilton–Jacobi–Bellman (HJB) equation. We then show that the optimal investment policy is a solution to a terminal value problem of an ordinary differential equation. In particular, explicit solutions are derived in some special cases and a series solution is obtained for the general case. Also, we propose a numerical method to solve the optimal investment and capital injection policies. Finally, a numerical study is carried out to illustrate the effect of the model parameters on the optimal policies. This is a joint work with Prof K C Yuen.
Starting Time: 8:00-12:00am March 25, 2016
Location: The conference room on the second floor