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|a (JST)2699929
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|a Pham, Huyên
|e verfasserin
|4 aut
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|a Minimizing Shortfall Risk and Applications to Finance and Insurance Problems
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|c 2002
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|a We consider a controlled process governed by Xx,θ= x + ∫θ dS + Hθ, where S is a semimartingale, Θ the set of control processes θ is a convex subset of L(S) and Hθ: θ∈Θ is a concave family of adapted processes with finite variation. We study the problem of minimizing the shortfall risk defined as the expectation of the shortfall (B - Xx, θ T)+ weighted by some loss function, where B is a given nonnegative measurable random variable. Such a criterion has been introduced by Follmer and Leukert [Finance Stoch. 4 (1999) 117-146] motivated by a hedging problem in an incomplete financial market context: Θ = L(S) and $H^\theta\equiv$ 0. Using change of measures and optional decomposition under constraints, we state an existence result to this optimization problem and show some qualitative properties of the associated value function. A verification theorem in terms of a dual control problem is established which is used to obtain a quantitative description of the solution. Finally, we give some applications to hedging problems in constrained portfolios, large investor and reinsurance models.
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|a Copyright 2002 Institute of Mathematical Statistics
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|a Shortfall Risk Minimization
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|a Semimartingales
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|a Optional Decomposition under Constraints
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|a Duality Theory
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|a Finance and Insurance
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|a Mathematics
|x Pure mathematics
|x Geometry
|x Geometric properties
|x Convexity
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|a Applied sciences
|x Engineering
|x Control engineering
|x Control theory
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|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
|x Stochastic processes
|x Martingales
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|a Economics
|x Economic disciplines
|x Financial economics
|x Insurance
|x Reinsurance
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|a Mathematics
|x Pure mathematics
|x Topology
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|a Political science
|x Government
|x Governance
|x Government budgets
|x Budget deficits
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|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
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|a Physical sciences
|x Physics
|x Mechanics
|x Density
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|a Economics
|x Economic disciplines
|x Financial economics
|x Finance
|x Financial management
|x Financial risk
|x Investment risk
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|a Philosophy
|x Logic
|x Logical topics
|x Formal logic
|x Mathematical logic
|x Mathematical set theory
|x Transfinite numbers
|x Infinity
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|a research-article
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|i Enthalten in
|t The Annals of Applied Probability
|d Institute of Mathematical Statistics
|g 12(2002), 1, Seite 143-172
|w (DE-627)270937838
|w (DE-600)1478737-4
|x 10505164
|7 nnns
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|g volume:12
|g year:2002
|g number:1
|g pages:143-172
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|u https://www.jstor.org/stable/2699929
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|d 12
|j 2002
|e 1
|h 143-172
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