Growth Versus Security in Dynamic Investment Analysis

This paper concerns the problem of optimal dynamic choice in discrete time for an investor. In each period the investor is faced with one or more risky investments. The maximization of the expected logarithm of the period by period wealth, referred to as the Kelly criterion, is a very desirable investment procedure. It has many attractive properties, such as maximizing the asymptotic rate of growth of the investor's fortune. On the other hand, instead of focusing on maximal growth, one can develop strategies based on maximum security. For example, one can minimize the ruin probability subject to making a positive return or compute a confidence level of increasing the investor's initial fortune to a given final wealth goal. This paper is concerned with methods to combine these two approaches. We derive computational formulas for a variety of growth and security measures. Utilizing fractional Kelly strategies, we can develop a complete tradeoff of growth versus security. The theory is applicable to favorable investment situations such as blackjack, horseracing, lotto games, index and commodity futures and options trading. The results provide insight into how one should properly invest in these situations.capital accumulation, fractional kelly strategies, effective growth-security tradeoff, blackjack, horseracing, lotto games, turn of the year effect

Wealth, Income, and Optimal Insurance

This article considers the decision to purchase insurance against possible losses of a property or wealth. The decision involves a standard economic trade-off between the benefit of protection against loss and the cost of insurance premium. The premium is paid out of the income and decreases the consumption of other goods and services, rather than out of wealth and decreases the property or wealth. The demand for insurance depends mainly on the income and preferences. As a result, unlike in the standard model, a fair premium is neither necessary nor sufficient for the optimality of full coverage insurance. Rather, the individuals with higher incomes purchase full coverage insurance even at unfair prices of insurance while the individuals with lower income purchase partial coverage insurance at a fair price. Copyright The Journal of Risk and Insurance, 2007.