Sensitivity analysis of utility-based prices and risk-tolerance wealth processes

Kramkov, Dmitry; Ŝırbu, Mihai

doi:10.1214/105051606000000529

Cited by 76 publications

(161 citation statements)

References 17 publications

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“…The duality theory above is the first step to perform the sensitivity analysis and first order expansion of the marginal utility-based prices as in [21] and [22] but in market models with proportional transaction costs. It is possible for us to discuss the sensitivity analysis of the marginal utilitybased price also on the transaction costs 0 < λ < 1.…”

Section: Then We Havementioning

confidence: 99%

Optimal Investment with Random Endowments and Transaction Costs: Duality Theory and Shadow Prices

Bayraktar

2016

SSRN Journal

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Abstract. This paper studies the utility maximization problem on the terminal wealth with both random endowments and proportional transaction costs. To deal with unbounded random payoffs from some illiquid claims, we propose to work with the acceptable portfolios defined via the consistent price system (CPS) such that the liquidation value processes stay above some stochastic thresholds. In the market consisting of one riskless bond and one risky asset, we obtain a type of the super-hedging result. Based on this characterization of the primal space, the existence and uniqueness of the optimal solution for the utility maximization problem are established using the convex duality analysis. As an important application of the duality theory, we provide some sufficient conditions for the existence of a shadow price process with random endowments in a generalized form similar to [5] as well as in the usual sense using acceptable portfolios.

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Section: Then We Havementioning

confidence: 99%

Optimal Investment with Random Endowments and Transaction Costs: Duality Theory and Shadow Prices

Bayraktar

2016

SSRN Journal

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“…It allows us to analyse the holder's optimal exercise policy through his forward indifference price. In Sections 3 and 4, we will focus our study on two specific financial applications: (i) the valuation of an American option written on a stock S with stochastic volatility under Stochastics: An International Journal of Probability and Stochastic Processes 745 forward performance criterion of exponential type [to be defined in (23)] and (ii) modelling early exercises of ESOs for criteria beyond the exponential forward performance.…”

Section: Forward Indifference Pricementioning

confidence: 99%

“…In the classical utility framework, as introduced by Davis [7], the marginal utility price represents the per-unit price that a risk-averse investor is willing to pay for an infinitesimal position in a contingent claim. In general, the marginal utility price is closely linked to both the investor's utility function and the market set-up, and it only becomes wealth independent under very special circumstances (see [23] for details). We adapt the classical definition to our forward performance framework and give a definition of the marginal forward indifference price.…”

Section: Introductionmentioning

confidence: 99%

Forward indifference valuation of American options

2012

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We analyse the valuation of American options under the forward performance criterion introduced by Musiela and Zariphopoulou [Quant. Finance 9 (2008), pp. 161-170]. In this framework, the performance criterion evolves forward in time without reference to a specific future time horizon, and may depend on the stochastic market conditions. We examine two applications: the valuation of American options with stochastic volatility and the modelling of early exercises of American-style employee stock options. We work with the assumption that forward indifference prices have sufficient regularity to be solutions of variational inequalities, and provide a comparative analysis between the classical and forward indifference valuation approaches. In the case of exponential forward performance, we derive a duality formula for the forward indifference price. Furthermore, we study the marginal forward performance price, which is related to the classical marginal utility price introduced by Davis (Mathematics of Derivatives Securities, Cambridge University Press, 1997, pp. 227 -254). We prove that, under arbitrary time-monotone forward performance criteria, the marginal forward indifference price of any claim is always independent of the investor's wealth and is represented as the expected discounted pay-off under the minimal martingale measure.

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“…Risk relates with the unpredictability of alternative outcomes [12]. More and more research works realize the importance of risk sensitivity for planners [13,24,27]. This is especially useful for planning domains with huge wins or loses of money, equipment or human life.…”

Section: Introductionmentioning

confidence: 99%

Towards a bridge between cost and wealth in risk-aware planning

2011

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Risk attitude reflects an intelligent agent's preference for different uncertain rewards. Cost is the resource consumed; wealth is the total amount of the resource an agent holds. In a risk-aware system whose risk attitude is not independent of wealth, utility is a function of wealth. Given the utility function is one-switch, if we simply use cost based utility functions for the reasoning, unless the initial wealth is zero, we cannot precisely obtain the optimum preference in every decision step. A bridge algorithm between cost and wealth helps us solve this problem. We provide a framework of the bridge algorithm for risk-aware Markov decision processes. We present an example of the block-world problem to explain the algorithm.An effective bridge algorithm helps planners to make reasonable decisions according to their risk attitudes, without changing the structure of Markov domains. A bridge between cost and wealth enables us to deal with planning domains using the powerful backward induction approach instead of decision tree. This will have profound theoretical and realistic influence on artificial intelligence, economics, health care, as well as other areas concerning risk.

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Sensitivity analysis of utility-based prices and risk-tolerance wealth processes

Cited by 76 publications

References 17 publications

Optimal Investment with Random Endowments and Transaction Costs: Duality Theory and Shadow Prices

Optimal Investment with Random Endowments and Transaction Costs: Duality Theory and Shadow Prices

Forward indifference valuation of American options

Towards a bridge between cost and wealth in risk-aware planning

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