Portfolio optimization with unobservable Markov-modulated drift process

Rieder, Ulrich; Bäuerle, Nicole

doi:10.1017/s0021900200000401

Cited by 49 publications

(82 citation statements)

References 7 publications

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“…This effect has also been reported in other situations with power utility (see e.g. Rieder & Bäuerle (2005)). Since the formula for (π * t ) is still quite complicated we did not try to prove this observation but we conjecture that it is true for reasonable parameters.…”

Section: An Examplesupporting

confidence: 84%

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Optimal Portfolios for Financial Markets with Wishart Volatility

Bäuerle¹,

Li²

2013

J. Appl. Probab.

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Abstract. We consider a multi asset financial market with stochastic volatility modeled by a Wishart process. This is an extension of the one-dimensional Heston model. Within this framework we study the problem of maximizing the expected utility of terminal wealth for power and logarithmic utility. We apply the usual stochastic control approach and obtain explicitly the optimal portfolio strategy and the value function in some parameter settings. In particular when the drift of the assets is a linear function of the volatility matrix. In this case the affine structure of the model can be exploited. In some cases we obtain a Feynman-Kac representation of the candidate value function. Though the approach we use is quite standard, the hard part is indeed to identify when the solution of the HJB equation is finite. This involves a couple of matrix analytic arguments. In a numerical study we discuss the influence of the investors' risk aversion on the hedging demand.

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Section: An Examplesupporting

confidence: 84%

“…This specific transformation has been used before by Zariphopoulou (2001) and in particular by Kraft (2005) in the one-dimensional Heston model and in Rieder & Bäuerle (2005) in a model with partial observation. Here we get exactly the same δ as in Kraft (2005), p. 305.…”

Section: Solutions Of the Hjb Equationmentioning

confidence: 99%

Optimal Portfolios for Financial Markets with Wishart Volatility

Bäuerle¹,

Li²

2013

J. Appl. Probab.

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“…which is called drift risk in Rieder and Bäuerle [16]. In particular, in the case of power utility the certainty equivalence principle does not hold.…”

Section: Remark 52 Inspection Of Equationmentioning

confidence: 99%

Portfolio Optimization Under Partial Information With Expert Opinions

Frey

Gabih

Wunderlich

2012

Int. J. Theor. Appl. Finan.

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This paper investigates optimal portfolio strategies in a market with partial information on the drift. The drift is modelled as a function of a continuous-time Markov chain with finitely many states which is not directly observable. Information on the drift is obtained from the observation of stock prices. Moreover, expert opinions in the form of signals at random discrete time points are included in the analysis. We derive the filtering equation for the return process and incorporate the filter into the state variables of the optimization problem. This problem is studied with dynamic programming methods. In particular, we propose a policy improvement method to obtain computable approximations of the optimal strategy. Numerical results are presented at the end.

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“…For a recent example of work on Markov Modulated Lévy processes in risk theory see Asmussen and Pihlsgård [4], and for a recent example of work on finance with a Markov Modulated Drift process see Rieder and Bäuerle [37]. For an introduction to this area, see Asmussen [1,2].…”

Section: Modulated Processesmentioning

confidence: 99%

On the large deviations of a class of modulated additive processes

2011

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Abstract. We prove that the large deviation principle holds for a class of processes inspired by semiMarkov additive processes. For the processes we consider, the sojourn times in the phase process need not be independent and identically distributed. Moreover the state selection process need not be independent of the sojourn times. We assume that the phase process takes values in a finite set and that the order in which elements in the set, called states, are visited is selected stochastically. The sojourn times determine how long the phase process spends in a state once it has been selected. The main tool is a representation formula for the sample paths of the empirical laws of the phase process. Then, based on assumed joint large deviation behavior of the state selection and sojourn processes, we prove that the empirical laws of the phase process satisfy a sample path large deviation principle. From this large deviation principle, the large deviations behavior of a class of modulated additive processes is deduced. As an illustration of the utility of the general results, we provide an alternate proof of results for modulated Lévy processes. As a practical application of the results, we calculate the large deviation rate function for a processes that arises as the International Telecommunications Union's standardized stochastic model of two-way conversational speech.Mathematics Subject Classification. 60F10, 60K15.

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Portfolio optimization with unobservable Markov-modulated drift process

Cited by 49 publications

References 7 publications

Optimal Portfolios for Financial Markets with Wishart Volatility

Optimal Portfolios for Financial Markets with Wishart Volatility

Portfolio Optimization Under Partial Information With Expert Opinions

On the large deviations of a class of modulated additive processes

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