We develop a model of portfolio choice to nest the views of Keynes, who advocates concentration in a few familiar assets, and Markowitz, who advocates diversification. We use the concepts of ambiguity and ambiguity aversion to formalize the idea of an investor's “familiarity” toward assets. The model shows that for any given level of expected returns, the optimal portfolio depends on two quantities: relative ambiguity across assets and the standard deviation of the expected return estimate for each asset. If both quantities are low, then the optimal portfolio consists of a mix of familiar and unfamiliar assets; moreover, an increase in correlation between assets causes an investor to increase concentration in familiar assets (flight to familiarity). Alternatively, if both quantities are high, then the optimal portfolio contains only the familiar asset(s), as Keynes would have advocated. In the extreme case in which both quantities are very high, no risky asset is held (nonparticipation). This paper was accepted by Brad Barber, Teck Ho, and Terrance Odean, special issue editors.

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Under a guaranteed annuity option, an insurer guarantees to convert a policyholder's accumulated funds to a life annuity at a fixed rate when the policy matures. If the annuity rates provided under the guarantee are more beneficial to the policyholder than the prevailing rates in the market the insurer has to make up the difference. Such guarantees are common in many US tax sheltered insurance products. These guarantees were popular in UK retirement savings contracts issued in the 1970's and 1980's when long-term interest rates were high. At that time, the options were very far out of the money and insurance companies apparently assumed that interest rates would remain high and thus that the guarantees would never become active. In the 1990's, as long-term interest rates began to fall, the value of these guarantees rose. Because of the way the guarantee was written, two other factors influenced the cost of these guarantees. First, strong stock market performance meant that the amounts to which the guarantee applied increased significantly. Second, the mortality assumption implicit in the guarantee did not anticipate the improvement in mortality which actually occurred.The emerging liabilities under these guarantees threatened the solvency of some companies and led to the closure of Equitable Life (UK) to new business. In this paper we explore the pricing and risk management of these guarantees.

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The traditional portfolio selection problem concerns an agent whose objective is to maximize the expected utility of terminal wealth over some horizon. This basic problem can be modified by adding constraints. In this paper we investigate the portfolio selection problem for an investor who desires to outperform some benchmark index with a certain confidence level. The benchmark is chosen to reflect some particular investment objective and it can be either deterministic or stochastic. The optimal strategy for this class of problems can lead to nonconvex constraints raising issues of existence and uniqueness. We solve this optimal portfolio selection problem and investigate the procedure for both deterministic and stochastic benchmarks.