Optimal Portfolio in Partially Observed Stochastic Volatility Models

Pham, Huyên

doi:10.1214/aoap/998926991

Cited by 82 publications

(71 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The random variable L is L B given in (26). For brevity of notation we shall often write F L B ≡ F B , with a similar convention for the value function, u L B ≡ u B , and other relevant quantities.…”

Section: Brownian Inside Informationmentioning

confidence: 99%

“…We give two applications of the enlargement formula, for L = L B in (26) and L = L S in (27), that pertain to our two optimal investment problems with privileged information.…”

Section: Initial Enlargements Of Filtrationsmentioning

confidence: 99%

“…There are many papers on partial information investment models [7,8,22,26,28,29], in which trading strategies are required to be adapted to the stock price filtration. There is also a rich literature on insider trading models, dating back to the classical equilibrium models of Kyle [21] and Back [5], built upon by Cho [11], Campi and Ç etin [10], Danilova [13], and Aase, Bjuland and Øksendal [1].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal investment with inside information and parameter uncertainty

Danilova¹,

Monoyios²,

Ng³

2010

Math Finan Econ

View full text Add to dashboard Cite

An optimal investment problem is solved for an insider who has access to noisy information related to a future stock price, but who does not know the stock price drift. The drift is filtered from a combination of price observations and the privileged information, fusing a partial information scenario with enlargement of filtration techniques. We apply a variant of the Kalman-Bucy filter to infer a signal, given a combination of an observation process and some additional information. This converts the combined partial and inside information model to a full information model, and the associated investment problem for HARA utility is explicitly solved via duality methods. We consider the cases in which the agent has information on the terminal value of the Brownian motion driving the stock, and on the terminal stock price itself. Comparisons are drawn with the classical partial information case without insider knowledge. The parameter uncertainty results in stock price inside information being more valuable than Brownian information, and perfect knowledge of the future stock price leads to infinite additional utility. This is in contrast to the conventional case in which the stock drift is assumed known, in which perfect information of any kind leads to unbounded additional utility, since stock price information is then indistinguishable from Brownian information.

show abstract

Section: Brownian Inside Informationmentioning

confidence: 99%

“…We give two applications of the enlargement formula, for L = L B in (26) and L = L S in (27), that pertain to our two optimal investment problems with privileged information.…”

Section: Initial Enlargements Of Filtrationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal investment with inside information and parameter uncertainty

Danilova¹,

Monoyios²,

Ng³

2010

Math Finan Econ

View full text Add to dashboard Cite

show abstract

“…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]. After the early paper [3], a DP-approach for a finite-horizon linear-Gaussian model with one unobserved factor that is independent of the risky asset has been used in [18].…”

Section: Introductionmentioning

confidence: 99%

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

Nagai

Runggaldier

2007

Progress in Probability

View full text Add to dashboard Cite

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.

show abstract

“…Examples for such models with partial observation can be found, for instance, in Lakner (1995), Elliott, Lahaie & Madan (1997), Elliott, Fischer & Platen (1999), Babbs & Nowman (1999), Frey & Runggaldier (1999, 2001, Karatzas & Zhao (2001), Pham & Quenez (2001), Nagai & Peng (2002), Bhar, Chiarella & Runggaldier (2004), Haussmann & Sass (2004), Kirch & Runggaldier (2004), Landen (2000), Runggaldier (2004), Gombani, Jaschke & Runggaldier (2005), Cvitanić, Rozovskii & Zaliapin (2006) and Bäuerle & Rieder (2007). For instance, of particular interest are the market prices of risk, which are important hidden quantities that the investors need for portfolio optimization.…”

Section: Introductionmentioning

confidence: 99%

A Benchmark Approach to Portfolio Optimization under Partial Information

Platen

Runggaldier

2007

Asia-Pacific Finan Markets

View full text Add to dashboard Cite

Abstract. This paper proposes a filtering methodology for portfolio optimization when some factors of the underlying model are only partially observed. The level of information is given by the observed quantities that are here supposed to be the primary securities and empirical log-price covariations. For a given level of information we determine the growth optimal portfolio, identify locally optimal portfolios that are located on a corresponding Markowitz efficient frontier and present an approach for expected utility maximization. We also present an expected utility indifference pricing approach under partial information for the pricing of nonreplicable contracts. This results in a real world pricing formula under partial information that turns out to be independent of the subjective utility of the investor and for which an equivalent risk neutral probability measure need not exist.

show abstract

Optimal Portfolio in Partially Observed Stochastic Volatility Models

Cited by 82 publications

References 26 publications

Optimal investment with inside information and parameter uncertainty

Optimal investment with inside information and parameter uncertainty

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

A Benchmark Approach to Portfolio Optimization under Partial Information

Contact Info

Product

Resources

About