Optimal Hedging and Valuation of Nontraded Assets

This paper examines a number of valuation problems faced by an expected-utility-maximizing investor who, over a given time horizon, is constrained to hold an asset which cannot be replicated by dynamic trading and which therefore does not have a unique no-arbitrage price. We first derive the private valuation which the investor assigns to the nontradedasset in order to determine his optimal investment in the traded assets. We thereby show that, as part of this portfolio, the investor hedges the private valuation process of the nontraded asset, rather than its market price process. We also study the price at which the investor would be willing to sell the nontraded asset if he were subsequently prohibited from trading in it, as well as the amount the investor would be willing to pay to removethe trading restriction. All three values are shown to depend in an intuitive manner on the investor's risk aversion, the residual risk of the nontraded asset unhedged by the traded assets, the difference between the constrained holding and optimal unconstrained holding of the asset and the length of the time horizon over which the asset cannot be traded.     

Optimal life insurance with no-borrowing constraints: duality approach and example

We solve an optimal portfolio choice problem under a no-borrowing assumption. A duality approach is applied to study a family’s optimal consumption, optimal portfolio choice, and optimal life insurance purchase when the family receives labor income that may be terminated due to the wage earner’s premature death or retirement. We establish the existence of an optimal solution to the optimization problem theoretically by the duality approach and we provide an explicitly solved example with numerical illustration. Our results illustrate that the no-borrowing constraints do not always impact the family’s optimal decisions on consumption, portfolio choice, and life insurance. When the constraints are binding, there must exist a wealth depletion time (WDT) prior to the retirement date, and the constraints indeed reduce the optimal consumption and the life insurance purchase at the beginning of time. However, the optimal consumption under the constraints will become larger than that without the constraints at some time later than the WDT.     

The Relations between Minimal Martingale Measure and Minimal Entropy Martingale Measure

We consider incomplete markets, where each risky asset fluctuation is a continuous semimartingale, and study a subset of Equivalent Local Martingale Measures in which Minimal Martingale Measure minimizes relative entropy.We also discuss, as special cases, some models with the risky assetfluctuation represented as a solution of some stochastic differential equations.Finally, we mention that the predictable representation property is essentialin order that Minimal Martingale Measure coincides with Minimal Entropy Martingale Measure.     

Risk sensitive asset management with transaction costs

This paper develops a continuous time risk-sensitive portfolio optimization model with a general transaction cost structure and where the individual securities or asset categories are explicitly affected by underlying economic factors. The security prices and factors follow diffusion processes with the drift and diffusion coefficients for the securities being functions of the factor levels. We develop methods of risk sensitive impulsive control theory in order to maximize an infinite horizon objective that is natural and features the long run expected growth rate, the asymptotic variance, and a single risk aversion parameter. The optimal trading strategy has a simple characterization in terms of the security prices and the factor levels. Moreover, it can be computed by solving a {\it risk sensitive quasi-variational inequality}. The Kelly criterion case is also studied, and the various results are related to the recent work by Morton and Pliska. Mansucript received: July 1998; final version received: January 1999     

Minimal Entropy Martingale Measures of Jump Type Price Processes in Incomplete Assets Markets

We consider the incomplete assets market and assume that the market has no-arbitrage. Then there are many equivalent martingale measures associated with the market. Among them, a probability measure which minimizes the relative entropy with respect to the original probability measure P, has a special importance. Such a measure is called the minimal entropy martingale measure (MEMM). In a previous paper, we have proved the existence theorem of the MEMM for the price processes given in the form of the diffusion type stochastic differential equation. In this article we discuss the MEMM of the jump type price processes, or especially of the log Lévy processes, and we give the explicit form of MEMM.     

动态不完全市场中不流动资产的定价

流动性对资产收益有重大影响,流动性好坏与资产能否流动是不同层面的问题,前者属于完全市场,后者属于不完全市场,但经典的金融经济学主要研究完全市场上的资产定价和最优组合策略。本文基于中国的现实制度背景,考察流动性受限对资产定价的影响,构建了动态不完全市场中不流动资产的定价模型及最优组合策略;证明了不流动性资产从根本上影响了最优组合策略,不流动资产折价率受到流动约束的时间长短、不流动资产收益的波动率等诸多参数的显著影响。     

Portfolio and welfare consequences of debt market dominance

The ability to issue debt that pays in units of the domestic good leads a country to accumulate a large and negative net foreign asset position while maintaining a positive position in equity. This debt market advantage also helps to explain the weak relationship between the real exchange rate and relative consumption. Our stylized model matches the key facts about the U.S. international portfolio, the U.S. real exchange rate, and explains nearly 50% of the observed variation in the valuation effects. We find that taxing bond market transactions increases the volatility of the exchange rate, capital flows and allocations. In contrast, taxing equity positions stabilizes the exchange rate and capital flows while having little impact on the allocation. Lastly, the paper describes a global solution method for portfolio problems under incomplete markets.     

Generalised Sharpe Ratios and Asset Pricing in Incomplete Markets

The paper presents an incomplete market pricingmethodology generating asset pricebounds conditional on the absence of attractiveinvestment opportunities in equilibrium.The paper extends and generalises the seminal article ofCochrane and Saá-Requejowho pioneered option pricing based on the absenceof arbitrage and high Sharpe Ratios. Ourcontribution is threefold:We base the equilibrium restrictions on an arbitrary utility function, obtaining theCochrane and Saá-Requejo analysis as a special case with truncated quadratic utility. We extend the definition of Sharpe Ratio from quadratic utility to the entire family of CRRA utility functions and restate the equilibrium restrictions in terms ofGeneralised Sharpe Ratios which, unlike the standard Sharpe Ratio, provide aconsistent ranking of investment opportunities even when asset returns are highlynon-normal. Last but not least, we demonstrate that for Itô processes theCochrane and Saá-Requejo price bounds are invariant to the choice of the utilityfunction, and that in the limit they tend to a unique price determined by theminimal martingale measure.     

Taxation of Interest Income

Why is interest income taxed so much more heavily than other forms of capital income? This differential tax treatment has generated substantial tax arbitrage, resulting in lower tax revenue, efficiency costs, and apparently net gains to rich borrowers and net losses to poor lenders, together suggesting that this tax treatment makes no sense on welfare grounds. In examining this argument more formally, this paper reveals two omitted considerations that can help explain the existing tax treatment. First, the forecasted increase in the market interest rate results in a redistribution from rich borrowers to poor lenders. Yet this redistribution comes at no marginal efficiency cost, starting from a situation with no distortions to portfolio choice, so at the margin dominates further redistribution through the income tax. In addition, information about an individual's portfolio choice reveals information about her earnings ability, even controlling for observed labor income, if those who are more able tend to be less risk averse. By making use of this extra information about earnings ability, the tax system can be better tailored to redistribute from able to less able, for any given efficiency cost.