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On the optimal hedge of a nontraded cash position

Article Abstract:

In this paper, we focus on the optimal demand for futures contracts by an investor with a logarithmic utility function who attempts to hedge a nontraded cash position. When the analysis is conducted in the "cash-commodity-price" space, we show that the value function associated with the Bernoulli investor program is not additively separable, thus suggesting that this investor hedges against shifts in the opportunity set as represented by the commodity price. By establishing the equivalence between the cash formulation of the problem and the wealth formulation, we are able to analyze the problem in the "wealth-commodity-price" space. In this space, we show the additive separability of the value function when the futures settlement price process is perfectly locally correlated with the commodity price process. The demand for futures in this instance is composed of (a) a mean-variance term and (b) a minimum-variance component that is a classic feature of models with nontraded assets. Since the first-best (nonmyopic) optimum is attained, however, the deviation from a mean-variance demand should not be interpreted as the expression of a nonmyopic behavior but rather as an attempt to restore a first-best optimum. On the other hand, when the correlation between the futures price and the underlying commodity price is imperfect, in general, the value function does not separate additively, the first-best solution cannot be attained, and the optimal futures trading strategy involves a hedging term against shifts in the opportunity set. (Reprinted by permission of the publisher.)

Usage, Hedging (Finance), Logarithmic functions

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Risk-based premiums for insurance guaranty funds

Article Abstract:

Insurance guaranty funds have been adopted in all states to compensate policyholders for losses resulting from insurance company insolvencies. The guaranty funds charge flat premium rates, usually a percentage of premiums. Flat premiums can induce insurers to adopt high-risk strategies, a problem that can be avoided through the use of risk-based premiums. This article develops risk-based premium formulas for three cases: (a) an ongoing insurer with stochastic assets and liabilities, (b) an ongoing insurer also subject to jumps in liabilities (catastrophes), and (c) a policy cohort, where claims eventually run off to zero. Premium estimates are provided and compared with actual guaranty fund assessment rates. (Reprinted by permission of the publisher.)

Management, Insurance industry, Surety bonds

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