Comparative Risk Aversion under Background Risks Revisited

This note determines a sufficient condition on (von Neumann-Morgenstern) utility functions to preserve (reserve) comparative risk aversion under general background risks. Our condition is weaker than the one determined by Nachman (1982, Journal of Economic Theory). Nachmanfs condition requires the monotonicity in the global sense, in other hand our condition only requires it in the local sense. And this generalization may make the condition on utility functions to hold the desirable property consisitent with the recent empirical observation.Background risk, comparative risk aversion, single crossing condition.

The Monotonicity of Asset Prices with Changes in Risk

The goal of this paper is the examination of the conditions on preferences to guarantee the monotonicity of asset prices, when their returns change in the sense of first- and second-order stochastic dominances.Asset Price; Comparative Statics; First-order Stochastic Dominance; Second-order Stochastic Dominance.

The Comparative Statics of Equilibrium Derivative Prices

We examine the conditions for preferences and risks that guarantee monotonicity of equilibrium derivative prices. In a Lucas economy with a derivative, we derive the equilibrium derivative price under expectation with respect to risk-neutral probability, and analyze comparative statics on the equilibrium derivative price based on the risk-neutral probability.Equilibrium Derivative Price, First-order Stochastic Dominance, Noise Risk, Risk-Neutral Probability.

Various Features of the Chooser Flexible Cap

In this paper, we theoretically look into various features of a chooser flexible cap. The chooser flexible cap is a financial instrument written on an underlying market interest rate index, LIBOR (London Inter-Bank Offer Rate). The chooser flexible cap allows a right for a buyer to exercise a limited and pre-determined number of the interim period caplets in a multiple-period cap agreement. While the chooser flexible cap is more flexible and cheaper instrument than the normal cap, its pricing is more complicated than the cap's because of its flexibility. So it may take long time for its price calculation. We can use the features to cut down the calculation time. At the same time the option holder can use the features for exercise strategies.chooser flexible cap, LIBOR, dynamic programming, exercise strategy.

The Comparative Statics on Asset Prices Based on Bull and Bear Market Measure

For single-period complete financial asset markets with representative investors, we introduce a bull market measure for uncertain state occurrence and its associated ordering between representative investors in markets based on their marginal rate of substitution between equilibrium consumption allocations among possible states. These concepts combine and generalize the likelihood-ratio-dominance relation between probability prospects of state occurrence and the Arrow-Pratt ordering of risk aversion in expected utility settings. By analyzing the comparative statics for bull market effects on equilibrium asset prices, we derive some monotone properties of the risk-free rate and discounted prices of dividend-monotone assets.Bull and Bear Market Measure, Comparative Statics, Equilibrium Asset Price, Dividend-Monotone Asset, Total Positivity of Order 2

Equilibrium execution strategies with generalized price impacts (Financial Modeling and Analysis)

This paper examines the execution problem of large traders with generalized price impact model. Constructing a model in a discrete-time setting, we solve this problem by applying the backward induction method of the dynamic programming. In this model, we formulate the expected utility maximization problem of multiple large traders as a Markov game and derive an equilibrium execution strategy at a Markov perfect equilibrium. This model enables us to investigate how the execution strategies and trade performances of these large traders are affected by the existence of other traders. Moreover, we find that these equilibrium execution strategies become deterministic when the total execution volumes of non large traders are deterministic. We also show, by some numerical examples, the comparative statics results with respect to several problem parameters