Anticipative portfolio optimization

We study a classical stochastic control problem arising in financial economics: to maximize expected logarithmic utility from terminal wealth and/or consumption. The novel feature of our work is that the portfolio is allowed to anticipate the future, i.e. the terminal values of the prices, or of the driving Brownian motion, are known to the investor, either exactly or with some uncertainty. Results on the finiteness of the value of the control problem are obtained in various setups, using techniques from the so-called enlargement of filtrations. When the value of the problem is finite, we compute it explicitly and exhibit an optimal portfolio in closed form.

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Anticipative portfolio optimization

Advances in Applied Probability ◽

10.2307/1428166 ◽

1996 ◽

Vol 28 (4) ◽

pp. 1095-1122 ◽

Cited By ~ 90

Author(s):

Igor Pikovsky ◽

Ioannis Karatzas

Keyword(s):

Brownian Motion ◽

Control Problem ◽

Closed Form ◽

Portfolio Optimization ◽

Stochastic Control ◽

Financial Economics ◽

Optimal Portfolio ◽

The Novel ◽

Terminal Wealth ◽

Terminal Values

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Malliavin calculus used to derive a stochastic maximum principle for system driven by fractional Brownian and standard Wiener motions with application

Random Operators and Stochastic Equations ◽

10.1515/rose-2020-2047 ◽

2020 ◽

Vol 28 (4) ◽

pp. 291-306

Author(s):

Tayeb Bouaziz ◽

Adel Chala

Keyword(s):

Brownian Motion ◽

Maximum Principle ◽

Control Problem ◽

Fractional Brownian Motion ◽

Stochastic Control ◽

Malliavin Calculus ◽

Stochastic Maximum Principle ◽

Hurst Parameter ◽

Principle Of Optimality ◽

Initial Cost

AbstractWe consider a stochastic control problem in the case where the set of the control domain is convex, and the system is governed by fractional Brownian motion with Hurst parameter {H\in(\frac{1}{2},1)} and standard Wiener motion. The criterion to be minimized is in the general form, with initial cost. We derive a stochastic maximum principle of optimality by using two famous approaches. The first one is the Doss–Sussmann transformation and the second one is the Malliavin derivative.

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Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem

Applied Mathematics and Computation ◽

10.1016/j.amc.2019.02.072 ◽

2019 ◽

Vol 355 ◽

pp. 282-298

Author(s):

Soukaina Douissi ◽

Jiaqiang Wen ◽

Yufeng Shi

Keyword(s):

Brownian Motion ◽

Control Problem ◽

Fractional Brownian Motion ◽

Stochastic Control ◽

Mean Field ◽

Stochastic Control Problem

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An Optimal Treatment Strategy for Diabetes

Journal of Biological System ◽

10.1142/s0218339003000920 ◽

2003 ◽

Vol 11 (04) ◽

pp. 419-425 ◽

Cited By ~ 1

Author(s):

Farai Nyabadza ◽

Edward M. Lungu

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Control Problem ◽

Stochastic Differential Equations ◽

Stochastic Control ◽

Treatment Strategy ◽

Sufficient Conditions ◽

Optimal Treatment ◽

The Body ◽

Optimal Treatment Strategy

Consider a system on n variables involved in the regulation of glucose in the body, whose concentrations are given by stochastic differential equations driven by m-dimensional Brownian motion. We formulate a stochastic control problem and give sufficient conditions for the existence of an optimal treatment strategy. We study the following problem: what treatment strategy for the n variables, maximizes the expected benefit from treatment.

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General Linear Quadratic Optimal Stochastic Control Problem Driven by a Brownian Motion and a Poisson Random Martingale Measure with Random Coefficients

Stochastic Analysis and Applications ◽

10.1080/07362994.2013.845106 ◽

2013 ◽

Vol 32 (1) ◽

pp. 88-109 ◽

Cited By ~ 12

Author(s):

Qingxin Meng

Keyword(s):

Brownian Motion ◽

Control Problem ◽

Stochastic Control ◽

Random Coefficients ◽

Optimal Stochastic Control ◽

General Linear ◽

Martingale Measure ◽

Linear Quadratic ◽

Stochastic Control Problem

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Connections Between Optimal Stopping and Stochastic Control II: Bounded-Variation Follower Problems

Advances in Applied Probability ◽

10.1017/s0001867800022072 ◽

1984 ◽

Vol 16 (1) ◽

pp. 16-16 ◽

Cited By ~ 1

Author(s):

Ioannis Karatzas ◽

Steven E. Shreve

Keyword(s):

Brownian Motion ◽

Control Problem ◽

Stochastic Control ◽

Bounded Variation ◽

Optimal Stopping ◽

Stochastic Control Problem

The stochastic control problem of tracking a Brownian motion by a process of bounded variation is reduced to a control problem with reflection at the origin, and the latter is related to a question of optimal stopping of Brownian motion absorbed at the origin. Direct probabilistic arguments can be used to show equivalences between the various problems.

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Connections between optimal stopping and stochastic control I. Monotone follower problems

Advances in Applied Probability ◽

10.1017/s0001867800022035 ◽

1984 ◽

Vol 16 (1) ◽

pp. 15-15

Author(s):

Joannis Karatzas ◽

Steven E. Shreve

Keyword(s):

Brownian Motion ◽

Control Problem ◽

Stochastic Control ◽

Optimal Stopping ◽

Optimal Solutions ◽

Stochastic Control Problem

The stochastic control problem of tracking a Brownian motion by a non-decreasing process (monotone follower) is related to a question of optimal stopping. Direct probabilistic arguments are employed to show that the two problems are equivalent and that both admit optimal solutions.

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