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This paper develops a general stochastic model of a frictionless security market with continuous trading. The vector price process is given by a semimartingale of a certain clr;zss, and the general stochastic integral is used to represent capital gains. Within the framework of this model, we discuss the modern theory of contingent claim valuation, including… (More)

- Stanley R. Pliska
- Math. Oper. Res.
- 1986

A pappr by the same authors in the 1981 volume of Stochastic Processes artd Their Applications presented a general model, based on martingales and stochastic integrals, for the economic problem of investing in a portfolio of securities. In particular, and using the terminology developed therein, that paper stated that every integrable contingent claim is… (More)

- Dong-Wan Tcha, Stanley R. Pliska
- Operations Research
- 1977

This paper develops a continuous time modeling approach for making optimal asset allocation decisions. Macroeconomic and "nancial factors are explicitly modeled as Gaussian stochastic processes which directly a!ect the mean returns of the assets. We employ methods of risk sensitive control theory, thereby using an in"nite horizon objective that is natural… (More)

- Tomasz R. Bielecki, Stanley R. Pliska
- Finance and Stochastics
- 2000

- Tomasz R. Bielecki, Daniel Hernández-Hernández, Stanley R. Pliska
- Math. Meth. of OR
- 1999

In this paper we extend standard dynamic programming results for the risk sensitive optimal control of discrete time Markov chains to a new class of models. The state space is only ®nite, but now the assumptions about the Markov transition matrix are much less restrictive. Our results are then applied to the ®nancial problem of managing a portfolio of… (More)

- Abel Cadenillas, Stanley R. Pliska
- Finance and Stochastics
- 1999

- Tomasz R. Bielecki, Stanley R. Pliska
- IEEE Trans. Automat. Contr.
- 2004

This paper presents an application of risk-sensitive control theory in financial decision making. A variation of Merton’s continuous-time intertemporal capital asset pricing model is developed where the infinite horizon objective is to maximize the portfolio’s risk adjusted growth rate. The resulting model is tractable and thus provides economic insight… (More)

This paper summarizes recent research on a new approach, namely, an equilibrium approach, to the valuation of fixed-rate mortgage contracts. Working in a discrete time setting with the mortgagor’s prepayment behavior described by a suitable intensity process and with exogenous mortgage rates, the value of the contract is derived in an explicit form that can… (More)