An agent can distribute his wealth between two investments, one with a fixed rate of return r and the other with a random rate of return (modeled as a diffusion) with mean r. The agent seeks to maximize total discounted utility from consumption over an infinite horizon. Consumption may be...

This paper presents an asymptotic analysis of a hierarchical manufacturing system with machines subject to breakdown and repair. The rate of change in machine states is much larger than the rate of fluctuation in demand and the rate of discounting of costs, and this gives rise to a limiting...

This paper solves a general consumption and investment decision problem in closed form. An investor seeks to maximize total expected discounted utility of consumption. There are N distinct risky investments, modeled by dependent geometric Brownian motion processes, and one risk-less...

A comparison of and the relationship between the Ito and Stratonovich formulations of stochastic integration is given. It is argued that generally the Ito formulation is appropriate for problems of finance and economics. The Black-Scholes option pricing problem is discussed in both frameworks...

The method of variational inequalities is a useful theoretical tool in stochastic control, but there are few problems in which this method leads to an explicit solution. We present such a problem drawn from portfolio management. An agent can distribute his wealth between two investments, one...

An asymptotic analysis of a hierarchical manufacturing system with machines subject to breakdown and repair is presented. The machine fluctuations are much faster than the accumulation and discounting of costs, and this gives rise to a limiting problem in which the stochastic machine...

This paper deals with the problem of the financial valuation of a firm and its shares of stock with general financing policies in a partial equilibrium framework. the model assumes a time-dependent discount rate and a general stochastic environment in a discrete-time setting. the fundamental...

Monte Carlo simulation is playing an increasingly important role in the pricing and hedging of complex, path dependent financial instruments. Low discrepancy simulation methods offer the potential to provide faster rates of convergence than those of standard Monte Carlo methods; however, in high...

General equilibrium models in which economic agents have finite marginal utility from consumption at the origin lead to financial assets having continuous prices with singular components. In particular, there is no bona fide "interest rate" in such models, although asset prices can be determined...