Showing papers by "Ioannis Karatzas published in 1994"
01 May 1994
TL;DR: In this paper, the problem of portfolio optimization under the drawdown constraint was studied, where the wealth process never falls below a fraction of its maximum-to-date, and one strives to maximize the long-term growth rate of its expected utility.
Abstract: We study the problem of portfolio optimization under the \drawdown constraint" that the wealth process never falls below a xed fraction of its maximum-to-date, and one strives to maximize the long-term growth rate of its expected utility. This problem was introduced and solved explicitly by Grossman and Zhou; we present an approach which simpli es and extends their results.
169 citations
TL;DR: This paper studies stationary noncooperative equilibria in an economy with fiat money, one nondurable commodity, countably many time periods, no credit or futures market, and a measure space of agents -- who may differ in their preferences and in the distributions of their (random) endowments.
Abstract: This paper studies stationary noncooperative equilibria in an economy with fiat money, one nondurable commodity, countably many time-periods, no credit or futures market, and a measure space of agents—who may differ in their preferences and in the distributions of their (random) endowments. These agents are immortal, and hold fiat money as a means of hedging against the random fluctuations in their endowments of the commodity. In the aggregate, these fluctuations offset each other, and equilibrium prices are constant. We carry out an equilibrium analysis that focuses on distribution of wealth, on consumption, and on price formation. A careful analysis of the one-agent, infinite-horizon optimization problem, and of the invariant measure for the associated optimally controlled Markov chain, leads by aggregation to a stationary noncooperative or competitive equilibrium. This consists of a price for the commodity and of a distribution of wealth across agents which, under appropriate simple strategies for the ...
78 citations
TL;DR: In this article, the authors present an approach to the general non-Markovian dynamic allocation problem, formulated in continuous time as a problem of stochastic control for multiparameter processes in the manner of Mandelbaum.
Abstract: We present an approach to the general, non-Markovian dynamic allocation (or multiarmed bandit) problem, formulated in continuous time as a problem of stochastic control for multiparameter processes in the manner of Mandelbaum. This approach is based on a direct, martingale study of auxiliary questions in optimal stopping. Using a methodology similar to that of Whittle and relying on simple time-change arguments, we construct Gittins-index-type strategies, verify their optimality, provide explicit expressions for the values of dynamic allocation and associated optimal stopping problems, explore interesting dualities and derive various characterizations of Gittins indices. This paper extends results of our recent work on discrete-parameter dynamic allocation to the continuous time setup; it can be read independently of that work.
72 citations
14 Dec 1994
TL;DR: In this article, the authors studied the stochastic control problem of maximizing expected logarithmic utility from terminal wealth and consumption, when the portfolio is allowed to anticipate the future; i.e., when the terminal values of the prices or of the driving Brownian motion are known to the investor, either exactly or with some noise.
Abstract: Studies the stochastic control problem of maximizing expected logarithmic utility from terminal wealth and/or consumption, when the portfolio is allowed to anticipate the future; i.e., when the terminal values of the prices or of the driving Brownian motion are known to the investor, either exactly or with some noise. Results on the finiteness of the value of the control problem in various setups are obtained, using techniques from the so-called enlargement of filtrations. >