Utility based optimal hedging in incomplete markets

Owen, Mark P.

doi:10.1214/aoap/1026915621

Cited by 37 publications

(33 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a general semimartingale context, the relationship between the MEMM and the utility indifference pricing problem is by now well known and comes from a fundamental duality result due to Delbaen et al [13] and Kabanov and Stricker [23] (see also [5,15,28,[34][35][36]). In Becherer [3] (see also Rouge and El Karoui [33] and [13]) many properties of the utility indifference price of a contingent claim is derived from this duality result.…”

Section: Introductionmentioning

confidence: 99%

A PDE representation of the density of the minimal entropy martingale measure in stochastic volatility markets

Benth

Karlsen

2005

Stochastics

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

A PDE representation of the density of the minimal entropy martingale measure in stochastic volatility markets

Benth

Karlsen

2005

Stochastics

View full text Add to dashboard Cite

“…Note also that (32) implies (28). We are interested in solving an optimal portfolio problem for an agent in a complete market with a single stock whose price process is a continuous semimartingale.…”

Section: Portfolio Optimisation Via Convex Dualitymentioning

confidence: 99%

“…For the incomplete market case, see the seminal paper by Karatzas et al [14] for markets with continuous price processes, and Kramkov and Schachermayer [16] for the case with general semimartingale price processes. For problems involving a terminal random endowment in the form of an F T -measurable random variable, contributions have been made by (among others) Hugonnier and Kramkov [9], Owen [28] and by Delbaen et al [6] for an agent with an exponential utility function. We shall use the results of [6] in Section 5, when we examine the exponential hedging of a contingent claim in a basis risk model.…”

Section: Incomplete Marketsmentioning

confidence: 99%

Optimal investment and hedging under partial and inside information

Albrecher¹,

Runggaldier²,

Schachermayer³

2009

Advanced Financial Modelling

View full text Add to dashboard Cite

This article concerns optimal investment and hedging for agents who must use trading strategies which are adapted to the filtration generated by asset prices, possibly augmented with some inside information related to the future evolution of an asset price. The price evolution and observations are taken to be continuous, so the partial (and, when applicable, inside) information scenario is characterised by asset price processes with an unknown drift parameter, which is to be filtered from price observations. We first give an exposition of filtering theory, leading to the Kalman-Bucy filter. We outline the dual approach to portfolio optimisation, which is then applied to the Merton optimal investment problem when the agent does not know the drift parameter of the underlying stock. This is taken to be a random variable with a Gaussian prior distribution, which is updated via the Kalman filter. This results in a model with a stochastic drift process adapted to the observation filtration, and which can be treated as a full information problem, and an explicit solution to the optimal investment problem is possible. We also consider the same problem when the agent has noisy knowledge at time 0 of the terminal value of the Brownian motion driving the stock. Using techniques of enlargement of filtration to accommodate the insider's additional knowledge, followed by filtering the asset price drift, we are again able to obtain an explicit solution. Finally we treat an incomplete market hedging problem. A claim on a non-traded asset is hedged using a correlated traded asset. We summarise the full information case, then treat the partial information scenario in which the hedger is uncertain of the true values of the asset price drifts. After filtering, the resulting problem with random drifts is solved in the case that each asset's prior distribution has the same variance, resulting in analytic approximations for the optimal hedging strategy.

show abstract

“…As Hobson (2004) has shown, the minimal entropy measure can be viewed as the q-optimal measure for q = 1, Q E = Q (1) . A well-known body of work (Karatzas et al (1991), Kramkov and Schachermayer (1999), Goll and Rüschendorf (2001), Bellini and Frittelli (2002), Delbaen et al (2002), Frittelli (2000), Owen (2002)) has established the fundamental duality relations between u(x) and v(η). The value functions u(x), v(η) are conjugate, inheriting these properties from U, V , and the optimal terminal wealth in (16), X * T , is related to the optimal dual measure Q * by…”

Section: The Dual Problemmentioning

confidence: 99%

Characterisation of optimal dual measures via distortion

Monoyios

2006

Decisions Econ Finan

View full text Add to dashboard Cite

We derive representations for optimal martingale measures in a two-factor Markovian model, by seeking ramifications of a distortion power solution (Zariphopoulou (2001)) of the primal utility maximisation problem, for the dual problem. This provides an alternative to existing methods in the literature for characterising optimal measures, and gives new results in the form of a novel representation for the dual stochastic control problem, and in the form of Esscher transform relations between the optimal measure and the minimal measure.

show abstract

Utility based optimal hedging in incomplete markets

Cited by 37 publications

References 13 publications

A PDE representation of the density of the minimal entropy martingale measure in stochastic volatility markets

A PDE representation of the density of the minimal entropy martingale measure in stochastic volatility markets

Optimal investment and hedging under partial and inside information

Characterisation of optimal dual measures via distortion

Contact Info

Product

Resources

About