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Convex duality in optimal investment and contingent claim valuation in illiquid markets

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Convex duality in optimal investment and contingent claim valuation in illiquid markets. / Pennanen, Teemu; Perkkiö, Ari-Pekka.

In: Finance and Stochastics , Vol. 22, No. 4, 10.2018, p. 733–771.

Research output: Contribution to journalArticle

Harvard

Pennanen, T & Perkkiö, A-P 2018, 'Convex duality in optimal investment and contingent claim valuation in illiquid markets', Finance and Stochastics , vol. 22, no. 4, pp. 733–771. https://doi.org/10.1007/s00780-018-0372-8

APA

Pennanen, T., & Perkkiö, A-P. (2018). Convex duality in optimal investment and contingent claim valuation in illiquid markets. Finance and Stochastics , 22(4), 733–771. https://doi.org/10.1007/s00780-018-0372-8

Vancouver

Pennanen T, Perkkiö A-P. Convex duality in optimal investment and contingent claim valuation in illiquid markets. Finance and Stochastics . 2018 Oct;22(4):733–771. https://doi.org/10.1007/s00780-018-0372-8

Author

Pennanen, Teemu ; Perkkiö, Ari-Pekka. / Convex duality in optimal investment and contingent claim valuation in illiquid markets. In: Finance and Stochastics . 2018 ; Vol. 22, No. 4. pp. 733–771.

Bibtex Download

@article{177b45af26d74e9b84b836a0456f63f9,
title = "Convex duality in optimal investment and contingent claim valuation in illiquid markets",
abstract = "This paper develops duality theory for optimal investment and contingentclaim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions decompose into three terms, corresponding to the agent{\textquoteright}s risk preferences, trading costs and portfolio constraints, respectively. The dual representations are shown to be valid when the market model satisfies an appropriate generalization of the noarbitrage condition and the agent{\textquoteright}s utility function satisfies an appropriate generalization of asymptotic elasticity conditions. When applied to classical liquid market models or models with bid–ask spreads, we recover well-known pricing formulas in terms of martingale measures and consistent price systems. Building on the general theory of convex stochastic optimization, we also obtain optimality conditions in terms of an extended notion of a “shadow price”. The results are illustrated by establishing the existence of solutions and optimality conditions for the nonlinear market models recently proposed in the literature. Our results allow significant extensions including nondifferentiable trading costs which arise, e.g., in modern limit order markets where the marginal price curve is necessarily discontinuous.",
author = "Teemu Pennanen and Ari-Pekka Perkki{\"o}",
year = "2018",
month = oct,
doi = "10.1007/s00780-018-0372-8",
language = "English",
volume = "22",
pages = "733–771",
journal = "Finance and Stochastics ",
number = "4",

}

RIS (suitable for import to EndNote) Download

TY - JOUR

T1 - Convex duality in optimal investment and contingent claim valuation in illiquid markets

AU - Pennanen, Teemu

AU - Perkkiö, Ari-Pekka

PY - 2018/10

Y1 - 2018/10

N2 - This paper develops duality theory for optimal investment and contingentclaim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions decompose into three terms, corresponding to the agent’s risk preferences, trading costs and portfolio constraints, respectively. The dual representations are shown to be valid when the market model satisfies an appropriate generalization of the noarbitrage condition and the agent’s utility function satisfies an appropriate generalization of asymptotic elasticity conditions. When applied to classical liquid market models or models with bid–ask spreads, we recover well-known pricing formulas in terms of martingale measures and consistent price systems. Building on the general theory of convex stochastic optimization, we also obtain optimality conditions in terms of an extended notion of a “shadow price”. The results are illustrated by establishing the existence of solutions and optimality conditions for the nonlinear market models recently proposed in the literature. Our results allow significant extensions including nondifferentiable trading costs which arise, e.g., in modern limit order markets where the marginal price curve is necessarily discontinuous.

AB - This paper develops duality theory for optimal investment and contingentclaim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions decompose into three terms, corresponding to the agent’s risk preferences, trading costs and portfolio constraints, respectively. The dual representations are shown to be valid when the market model satisfies an appropriate generalization of the noarbitrage condition and the agent’s utility function satisfies an appropriate generalization of asymptotic elasticity conditions. When applied to classical liquid market models or models with bid–ask spreads, we recover well-known pricing formulas in terms of martingale measures and consistent price systems. Building on the general theory of convex stochastic optimization, we also obtain optimality conditions in terms of an extended notion of a “shadow price”. The results are illustrated by establishing the existence of solutions and optimality conditions for the nonlinear market models recently proposed in the literature. Our results allow significant extensions including nondifferentiable trading costs which arise, e.g., in modern limit order markets where the marginal price curve is necessarily discontinuous.

U2 - 10.1007/s00780-018-0372-8

DO - 10.1007/s00780-018-0372-8

M3 - Article

VL - 22

SP - 733

EP - 771

JO - Finance and Stochastics

JF - Finance and Stochastics

IS - 4

ER -

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