this paper to a stochastic time-dependent situation, simply by a suitable choice of the underlying measure space. In addition to the space\Omega of states of nature, whose distribution is given by the (probability) measure ¯, there is now also a time interval [0; T ] and a filtration fF t : t 2 [0; T ]g of information oe-algebras

We consider the problem of replicating the payoffs from variable annuities with a continuous cash flow given by a function of some traded asset's price. The standard approaches involve either dynamic trading in this underlying asset or a static position in a continuum of options of all strikes and maturities. We present an alternative approach which combines dynamic trading in the underlying asset with a static position in options of a single maturity. In many instances, our approach yields explicit valuation formulas and hedging strategies when the volatility of the underlying is an arbitrary function of its price.

In recentyears results from the theory of martingales has been successfully applied to problems in financial economics. In the present paper we showhow efficient and elegant this "martingale technology" can be when solving for complex options. In particular we provide closed form solutions for several new classes of exotic options including the cliquet, the ladder, the discrete shout and the discrete lookback. We also provide a derivation of the price of an option on the maximum of n assets to demonstrate the power of the multi-dimensional Girsanov theorem. Although some of the results presented are well known, the treatment of the material in this paper is new in that it focuses on the application of the martingale technology to concrete problems in option pricing, methods that until nowhave mostly been used for purely theoretical purposes.

This paper extends Merton’s continuous time (instantaneous) mean-variance analysis and the mutual fund separation theory. Given the existence of a Markovian state price density process, the optimal portfolios from concave utility maximization are instantaneously mean-variance efficient independent of the concave utility function’s form. The Capital Asset Pricing Model holds with the market portfolio induced by the growth optimal portfolio. The Markowitz-Tobin mutual fund separation is extended to include the lognormal assumption for asset prices as a special case. Closed form solutions to the expected utility maximization of terminal portfolio value are derived. We present an example in which the state price processes are specified as a multivariate geometric Brownian motion and the asset prices follow a multivariate diffusion process with relatively general parameters.

This article highlights the importance of investors’downside-risk concerns, and examines optimal investment behaviors in a dynamic downside-risk framework. The authors does not only derive an analytical expression of investors ’ optimal behaviors, but also provide economic insights of the properties of the downside risk measure and optimal investment strategies using comparative statics. It sheds light on both academic and practical applications of dynamic below-target semi-variance model to the …elds of risk management and investment decision making.

We consider the problem of replicating the payoffs from variable annuities with a continuous cash flow given by a function of some traded asset’s price. The standard approaches involve either dynamic trading in this underlying asset or a static position in a continuum of options of all strikes and maturities. We present an alternative approach which combines dynamic trading in the underlying asset with a static position in options of a single maturity. In many instances, our approach yields explicit valuation formulas and hedging strategies when the volatility of the underlying is an arbitrary function of its price.

We analyze general stochastic optimization financial problems under constraints in a general framework, which includes financial models with some “imperfection”, such as constrained portfolios, labor income, random endowment and large investor models. By using general optional decomposition under constraints in a multiplicative form, we first develop a dual formulation under minimal assumption modeled as in Pham and Mnif (2002) [Ph-M], Long (2002) [L02a]. We then are able to prove an existence and uniqueness of an optimal solution to primal and to the corresponding dual problem. An optimal investment to the original problem then can be found by convex duality, similarly to the case considered by Kramkov and Schachermayer (1999) [K-Sch].

We build a theory of reference-dependent preferences based on adjustment costs in consumption. The main contribution of the theory is that it endogenizes the evolution of the reference point. The reference point generated by our model exhibits several features exogenously assumed in existing theories: it (1) re‡ects recent expectations, (2) depends on past consumption levels, and (3) diminishes in importance when agents experience large shocks. When the ratio of idiosyncratic to aggregate risk is large, the model is approximately equivalent to standard habit formation speci…cations in which the reference point is a weighted average of past consumption. We illustrate the implications of endogenizing the reference point using three applications: aggregate consumption dynamics, changes in policy parameters, and the welfare cost of shocks. In each application, our model of endogenous reference points con…rms certain intuitions from existing theories but yields some starkly di¤erent predictions. For example, reducing idiosyncratic risk can raise the welfare cost of aggregate shocks by making reference points more persistent.