Stochastic programs without duality gaps

Pennanen, Teemu; Perkkiö, Ari-Pekka

doi:10.1007/s10107-012-0552-9

Cited by 32 publications

(64 citation statements)

References 23 publications

(74 reference statements)

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“…This is done by embedding (ALM) in the general stochastic optimization framework of [46]. Besides existence of optimal trading strategies, we find that the value function ϕ is lower semicontinuous with respect to convergence in measure on the space M of adapted claims.…”

Section: Existence Of Optimal Trading Strategiesmentioning

confidence: 97%

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Optimal investment and contingent claim valuation in illiquid markets

Pennanen

2014

Finance Stoch

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This paper extends basic results on arbitrage bounds and attainable claims to illiquid markets and general swap contracts where both claims and premiums may have multiple payout dates. Explicit consideration of swap contracts is essential in illiquid markets where the valuation of swaps cannot be reduced to the valuation of cumulative claims at maturity. We establish the existence of optimal trading strategies and the lower semicontinuity of the optimal value of optimal investment under conditions that extend the no-arbitrage condition in the classical linear market model. All results are derived with the "direct method" without resorting to duality arguments.

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Section: Existence Of Optimal Trading Strategiesmentioning

confidence: 97%

“…By [48, 14.32, 14.36, 14.44], f is an F-measurable normal integrand. We are thus in the general setting of [46] so by [46,Theorem 2], ϕ is lower semicontinuous and the infimum is attained for every c ∈ M provided…”

Section: Existence Of Optimal Trading Strategiesmentioning

confidence: 99%

Optimal investment and contingent claim valuation in illiquid markets

Pennanen

2014

Finance Stoch

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“…The following result from [11] relaxes the compactness assumptions made in [21] and [7]. In the context of financial mathematics, this allows for various extensions of certain fundamental results in financial mathematics; see [11] for details. An extension to nonconvex stochastic optimization can be found in [12].…”

Section: Dual Dynamic Programmingmentioning

confidence: 99%

“…Several examples can be found in the above references. Applications to financial mathematics are given in [9][10][11].…”

Section: Eh(x) := H(x(ω) ω)D P(ω)mentioning

confidence: 99%

Shadow price of information in discrete time stochastic optimization

Pennanen

Perkkiö

2017

Math. Program.

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The shadow price of information has played a central role in stochastic optimization ever since its introduction by Rockafellar and Wets in the mid-seventies. This article studies the concept in an extended formulation of the problem and gives relaxed sufficient conditions for its existence. We allow for general adapted decision strategies, which enables one to establish the existence of solutions and the absence of a duality gap e.g. in various problems of financial mathematics where the usual boundedness assumptions fail. As applications, we calculate conjugates and subdifferentials of integral functionals and conditional expectations of normal integrands. We also give a dual form of the general dynamic programming recursion that characterizes shadow prices of information. The second author is grateful to the Einstein Foundation for the financial support. Keywords B Teemu Pennanen

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“…We extend the existence results of [40] and [18] by relaxing their assumptions on compactness and convexity. We follow the arguments of [30] where it was assumed that the objective is given in terms of a convex integrand that has an integrable lower bound. In the context of utility maximization, the boundedness means that the utility functions are bounded from above but we pose no restrictions on its domain.…”

Section: Introductionmentioning

confidence: 99%

Existence of solutions in non-convex dynamic programming and optimal investment

2016

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We establish the existence of minimizers in a rather general setting of dynamic stochastic optimization in finite discrete time without assuming either convexity or coercivity of the objective function. We apply this to prove the existence of optimal investment strategies for non-concave utility maximization problems in financial market models with frictions, a first result of its kind. The proofs are based on the dynamic programming principle whose validity is established under quite general assumptions.

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Stochastic programs without duality gaps

Cited by 32 publications

References 23 publications

Optimal investment and contingent claim valuation in illiquid markets

Optimal investment and contingent claim valuation in illiquid markets

Shadow price of information in discrete time stochastic optimization

Existence of solutions in non-convex dynamic programming and optimal investment

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