Academic journal article Journal of Risk and Insurance

An OLG Model for Optimal Investment and Insurance Decisions

Academic journal article Journal of Risk and Insurance

An OLG Model for Optimal Investment and Insurance Decisions

Article excerpt

INTRODUCTION

Purchasing insurance has become one of the primary means of investment and risk management for individuals (or families). They purchase survival insurance (pension) to cover daily living expenses when they become old, and life insurance to protect their dependents against financial hardship in the event of their sudden death. According to the NAIC statistics, for 2008, 2009, and 2010, the total insurance premium income in the United States reached $8,028 billion, $7,221 billion, and $7,202 billion, respectively, (1) which accounted for 5.6 percent, 5.1 percent, and 5.5 percent of the nation's GDP, respectively. Statistics from the Bureau of Labor Statistics show that about 12 percent of the total expenditure is on private insurance, life insurance, and pension fund expenses in household consumption.

Since 1960s, many researchers have studied individuals' optimal decision-making process on their expenditure, such as consumption, investment, insurance purchasing, and so on. Yaari (1965), who's study is a starting point for modern research on the demand for life insurance, considered the problem of life insurance in the classical framework of consumption and investment. He assumed that an individual, whose objective was to maximize his lifelong utility, had an uncertain lifetime, and this was the only source of uncertainty. And further, annuity, which had a higher interest rate than bank deposit, was the only product on the market. Under these assumptions, he concluded that annuitization was the best strategy to generate lifetime income. Yaari addressed the optimal insurance and consumption choices under uncertainty lifetime, which pioneered the consumption-insurance issues, but with some flaws. Leung (1994) pointed out that an interior solution to optimize the lifelong utility does not exist. Hakansson (1969) also assumed that the individuals' lifetime was uncertainty and researched the insurance problem in the framework of investment and consumption. Unlike Yaari, Hakansson constructed a discrete model and assumed that the remaining lifetime was subject to a known probability distribution. He derived the optimal strategy and the boundary conditions for purchasing insurance products under the four possible combinations of bequest motive/no bequest motive and insurance/no insurance. Following the framework of Hakansson, Fischer (1973) continued the research on consumption, investment, and insurance purchases. Fischer emphasized comparative statics and dynamics of the insurance demand functions, rather than on the existence of a solution to the problem. Richard (1975) extended the continuous consumption-investment model of Merton (1971), added life insurance in the asset portfolio, and derived the optimal consumption, stock purchases, and demands for life insurance. He assumed that individuals could buy or sell insurance products whose period was instantaneous and claimed that the uncertainty of remaining lifetime would not affect the individual's investment decision. Campbell (1980) analyzed households' optimal reaction to labor income uncertainty derived from the possibility of their wage earners' nonsurvival. In Campbell's model, individuals' demand of insurance was based on the consideration of the daily life expenses of other family members. Campbell derived the insurance demand equation in the case of single- and multiphase. Following Campbell, Lewis (1989) believed that the income of a household was uncertain due to the uncertainty of the breadwinner's lifetime and that the household purchased insurance to avoid this uncertainty. He built the objective function from the beneficiary's perspective. This approach was different from Campbell and resulted in a different insurance demand function. Babbel and Ohtsuka (1989) built a multiperiod model that was used to analyze various aspects of whole life and term insurance contracts within the context of the lifetime consumption-investment problem. …

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