Hong Mao

Optimal Decision on Dynamic Insurance Price and Investment Portfolio of an Insurer in a Competitive Market

In this article, we establish a model of insurance pricing with the assumptions that the insurance price, investment returns and insured losses are correlated stochastic processes, while also considering the affect of the demand on the price. The objective of the pricing model is to maximize the expected utility of the terminal wealth of an insurer. We construct a Hamilton–Jacobi–Bellman (HJB) equation and determine the optimal price of an insurance product and optimal investment portfolio of an insurer simultaneously by solving that HJB equation. We also carry out sensitivity analysis. The results of our analysis show that elasticity of insurance demand greatly affects the optimal solutions. Notably, quantity of insurance demanded affects the optimal allocation to risky assets in the insurer’s investment portfolio. Therefore, the demand function for insurance must be considered in management of insurance firm. Our results also show that the drift and volatility of the process of insurance price will affect the investment strategy, in addition to the effect of the drift and volatility of investment process itself. Finally, the drift and volatility of investment stochastic process will affect the insurance price in the cases when the elasticity of demand is large, but that influence is negligible with small elasticity of demand.

Risk Management for Insurers: Integration of Capital Management and Product Design

In this paper, we extend Kliger and Levikson’s approach for pricing insurance contracts by considering the influence of capital held by an insurance firm on the price of insurance contracts, and we determine how to arrive at the optimal price, number of policies and capital level of the insurers. We also extend the above approach to a multi-line insurance firm. Our results are different from most of existing literature on capital allocation -- we show that even with multiple lines of business, the insurers still only need to hold a single overall capital allocation covering all of its lines of business, since the cost of capital and the probability of bankruptcy only depend on the total capital. Finally, our results also show that capital is an expensive resource, therefore, integrating capital management and optimization of price and product mix may be the most effective strategy of risk management especially when the capital cost is high.

Considering Part-Time Work after Retirement: Should I Stay or Should I Go?

In this article, we use dynamic leisure preference to study the optimal retirement decision with consideration of part-time work after the “official” retirement. We also consider a risky investment besides risk-free investment. and allow investor borrowing money at risk-free interest rate. Our results indicate that the optimal retirement age is very sensitive to the following parameters: coefficient of risk version, the leisure, rate after retirement, coefficient of survival function (describing the individual’s mortality), interest rate and discount rate, and is especially sensitive to the drift of return rate of risky assets invested. Our results also show that mortality improvement greatly affect all other optimal solutions except optimal retirement age, but have small affect on optimal retirement age.

Optimal Economic Capital Under the Consideration of Systemic Risk

In this article, we discuss the determination of the optimal capital level under the consideration of systemic risk. We establish several models for calculating optimal capital level in different conditions including without constraint, with constraints of the value of systemic risk (STVaR) and the value of expected shortfall of systemic risk (STVaR) respectively. We also carry out some numerical analysis with the data from 61 main banks of U.S. and Canada.

Unified and Dynamic Monitoring of Solvency of Property and Liability Insurance Companies

Abstract Dynamic monitoring is an accepted and widely used technique of industrial quality control. In this work, we apply dynamic monitoring to monitor and predict insurer financial strength. We propose a new statistic that combines means, variances, and co-variances of multivariate financial indices as a type of quality control tool. We employ data for US property and casualty insurers for the period 2001 through 2010 to determine the control regions, and we provide two examples to illustrate the application of our proposed methodology. We also demonstrate that the proposed methodology is especially suitable to emerging insurance markets, although it is applicable for developed insurance markets as well.

Determining the Insurer’s Optimal Investment and Reinsurance Strategy Based on Stochastic Differential Game

This paper seeks to determine the optimal investment and reinsurance strategy for an insurer whose wealth follows a diffusion process. We extend Zhang and Siu (2009) in our model and establish the Hamilton†Jacobi†Bellman†Isaacs equations, for which we obtain the optimal solutions. The optimal solutions indicate the use of reinsurance and investment allocation to risky assets. Results show that when the utility function of the insurer’s terminal wealth is exponential, the optimal solutions are positively correlated with time, but independent of the insurer’s wealth. However, for the power utility function, the optimal solutions are uncorrelated with time and are increasing functions of the insurer’s wealth. We also demonstrate that the insurer’s investment and reinsurance strategies are dependent on the risk†free interest rate.

The Determination of the Necessary Economic Capital, Investment and Reinsurance Strategies for Insurance Companies

In this article, we establish integrated models to determine the necessary economical capital, investment and reinsurance strategies concurrently based on the criteria of minimizing the total frictional cost, Solvency II and Swiss Solvency Test respectively. We consider different structures of assets and liabilities for both property-liability insurers and life insurers. We numerically analyze the effect of several critical parameters on the optimal investment and reinsurance strategies and the capital level. The results show that if the reinsurance cost is low or the frictional cost of capital is high or both, reinsurance can be an effective instrument for capital management. The results also show that the regulatory capital level based on either Solvency II or Swiss Solvency Test tends to be more prudent to the risks than the capital level determined by only minimizing the total frictional cost.

Pricing annuity insurance integrating mortality improvement risk, interest rate risk, insolvency risk and insurance demand

In this paper, we discuss the pricing of annuity insurance. We emphasize how to consider the mortality risk in pricing model and at the same time, integrate interest rate risk, insolvency risk and insurance demand. The results of our analysis show that it is beneficial to both of consumers and insurers if considering the factor of mortality improvement in pricing of annuity insurance.

Insurance pricing, reinsurance and investment decision based on the Mutual Benefit of the insurer and the customer

In this article, we establish an optimal decision model of insurance pricing, reinsurance and investment based on the mutual benefits of the insurer and the customer instead of only considering the benefit of the insurer, which is conformed with one of important objective of financial institution, that is, customer-oriented. We assume that the price and the claim loss rate are independent stochastic processes and n kinds risky assets are correlated stochastic processes. The main objective of our model is to minimize the expected utility of the premium paid by the customer in a bounded horizon and to maximize the utility of the relative terminal wealth of the insurer respect to the price of insurance. We construct a HJB equation and determine the optimal price of the insurance products, the optimal reinsurance strategy and the optimal investment portfolio of the insurer simultaneously by solving Hamilton-Jacobobi-Bellman HJB equation. Finally, we use an example to illustrate its application.

The Determination of Optimal Retirement Age Using Optimal Control Theory

In this paper, we discuss how to determine optimal retirement age using an optimal control theory. We establish a life cycle model and analyze the factors of consumption, leisure, saving, mortality and retirement behaviors simultaneously with an orthogonal–array experimental design. Our results show that the initial salary level and the growth rate of salary are the most important determining factors of the optimal retirement age. The initial consumption level and the interest rate are also important factors affecting optimal retirement age. The mortality improvement has a minor effect on the optimal retirement age. The effects of the Social Security on the optimal retirement age depend on the Social Security tax and the Social Security benefit.