Utility maximization with partial information

Lakner, Peter

doi:10.1016/0304-4149(94)00073-3

Cited by 152 publications

(116 citation statements)

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“…See also Feldman (1989Feldman ( , 1992Feldman ( , 2003 for further applications to general equilibrium models, and Feldman (2007) for a critical discussion and an overview. Two basic references for the general theory are Lakner (1995Lakner ( , 1998. In Lakner (1995), the author studies the problem in general terms and derives, using martingale methods, the structure of the optimal investment and consumption strategies.…”

Section: Introductionmentioning

confidence: 99%

“…Two basic references for the general theory are Lakner (1995Lakner ( , 1998. In Lakner (1995), the author studies the problem in general terms and derives, using martingale methods, the structure of the optimal investment and consumption strategies. Explicit 2 results are then obtained for log and power utility in a model where the rates of returns are constant random variables.…”

Section: Introductionmentioning

confidence: 99%

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Optimal investment under partial information

2010

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Reprinted from Mathematical Methods in Operations Research (2010), Volume 71, Number 2, 371-399 Terms of use: Documents in AbstractWe consider the problem of maximizing terminal utility in a model where asset prices are driven by Wiener processes, but where the various rates of returns are allowed to be arbitrary semimartingales. The only information available to the investor is the one generated by the asset prices and, in particular, the return processes cannot be observed directly. This leads to an optimal control problem under partial information and for the cases of power, log, and exponential utility we manage to provide a surprisingly explicit representation of the optimal terminal wealth as well as of the optimal portfolio strategy. This is done without any assumptions about the dynamical structure of the return processes. We also show how various explicit results in the existing literature are derived as special cases of the general theory. * Support from the Tom Hedelius and Jan Wallander Foundation is gratefully acknowledged. The authors are very grateful to the Associate editor and two anonymous referees for a number of very helpful comments.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal investment under partial information

2010

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“…While DP has a longer tradition in general, also MM has been applied already since some time for the cases when the drift/appreciation rate in a diffusion-type market model is supposed to be an unknown constant, a hidden finite-state Markov process, or a linear-Gaussian factor process. Along this line are the papers [9], [10], [8], [22] and, more recently, [5] and [20]. The case when the volatility is driven by a hidden process is studied in [16].…”

Section: Introductionmentioning

confidence: 99%

PDE Approach to Utility Maximization for Market Models with Hidden Markov Factors

Nagai

Runggaldier

2007

Progress in Probability

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Abstract. We consider the problem of maximizing expected utility from terminal wealth for a power utility of the risk-averse type assuming that the dynamics of the risky assets are affected by hidden "economic factors" that evolve as a finite-state Markov process. For this partially observable stochastic control problem we determine a corresponding complete observation problem that turns out to be of the risk sensitive type and for which the Dynamic programming approach leads to a nonlinear PDE that, via a suitable transformation, can be made linear. By means of a probabilistic representation we obtain a unique viscosity solution to the latter PDE that induces a unique viscosity solution to the former. This probabilistic representation allows to obtain, on one hand regularity results, on the other a computational approach based on Monte Carlo simulation. Mathematics Subject Classification (2000). Primary 93E20; Secondary 91B28, 49L20, 49L25.

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“…Current equilibrium prices thus reflect all possible 1 Brennan and Xia (2001), Bullard and Duffy (2001), Timmermann (1993Timmermann ( , 1996Timmermann ( , 2001, and Veronesi (1999) are among the contributions on the topic. 2 For instance, Lakner (1995) investigates consumption and portfolio choice in a finite horizon model in which agents have power utility. While asset prices are observable, their drift and the price shocks are not.…”

Section: Introductionmentioning

confidence: 99%

Properties of equilibrium asset prices under alternative learning schemes

Guidolin

Timmermann

2007

Journal of Economic Dynamics and Control

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This paper characterizes equilibrium asset prices under adaptive, rational and Bayesian learning schemes in a model where dividends evolve on a binomial lattice. The properties of equilibrium stock and bond prices under learning are shown to differ significantly. Learning causes the discount factor and risk-neutral probability measure to become path-dependent and introduces serial correlation and volatility clustering in stock returns. We also derive conditions under which the expected value and volatility of stock prices will be higher under learning than under full information. Finally, we investigate restrictions on prior beliefs under which Bayesian and rational learning lead to identical prices and show how the results can be generalized to more complex settings where dividends follow either multi-state i.i.d. distributions or multi-state Markov chains.. . * We thank two anonymous referees,

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Utility maximization with partial information

Cited by 152 publications

References 7 publications

Optimal investment under partial information

Optimal investment under partial information

PDE Approach to Utility Maximization for Market Models with Hidden Markov Factors

Properties of equilibrium asset prices under alternative learning schemes

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