Displaying similar documents to “Comparison principle approach to utility maximization”

Valuation and optimal design to defaultable security

Jianhui Huang, Na Li (2006)

Applicationes Mathematicae

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Herein, we develop a backward stochastic differential equation (BSDE) valuation of securities with default risk. Consequently, the optimal recovery problem with quasi-linear utility functions is discussed with the help of the stochastic maximum principle. Finally, two important examples: the exponential and power utility cases are studied and their business implications are considered.

An asset – liability management stochastic program of a leasing company

Tomáš Rusý, Miloš Kopa (2018)

Kybernetika

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We build a multi-stage stochastic program of an asset-liability management problem of a leasing company, analyse model results and present a stress-testing methodology suited for financial applications. At the beginning, the business model of such a company is formulated. We introduce three various risk constraints, namely the chance constraint, the Value-at-Risk constraint and the conditional Value-at-Risk constraint along with the second-order stochastic dominance constraint, which...

Risk minimizing strategies for a portfolio of interest-rate securities

Andrzej Palczewski (2008)

Banach Center Publications

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The paper presents an application of stochastic control methods to fixed income management in an incomplete market with external economic factors. The objective of an investor is the minimization of a shortfall risk. The problem is reduced to the multidimensional Bellman equation. It is shown that for a large class of loss functions the equation possesses a continuous solution. We also consider loss functions from the HARA class and prove that for such functions the Hamilton-Jacobi-Bellman...

Newsboy Problem: Viability of Optimal Initial Selling Price and Ordering Policies in the Presence of Exogenous Price Decline and Random Lead Time

Ningombam Sanjib Meitei, Snigdha Banerjee (2013)

RAIRO - Operations Research - Recherche Opérationnelle

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Analysis of empirical sales data lead us to consider newsboy model for four practical market conditions arising from the presence/absence of stochastic lead time and exogenous linear temporal decline in selling price when distribution of the stochastic demand depends upon initial selling price. Viability of the solutions is discussed for three strategies of obtaining optimal initial selling price and/or ordering quantity. Numerical studies are conducted to assess the effects of lead...

Optimal investment under stochastic volatility and power type utility function

Benchaabane, Abbes, Benchettah, Azzedine (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20. In this work we will study a problem of optimal investment in financial markets with stochastic volatility with small parameter. We used the averaging method of Bogoliubov for limited development for the optimal strategies when the small parameter of the model tends to zero and the limit for the optimal strategy and demonstrated the convergence of these optimal strategies.

Optimal investment strategy for a non-life insurance company: quadratic loss

Łukasz Delong (2005)

Applicationes Mathematicae

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The aim of this paper is to construct an optimal investment strategy for a non-life insurance business. We consider an insurance company which provides, in exchange for a single premium, full coverage to a portfolio of risks which generates losses according to a compound Poisson process. The insurer invests the premium and trades continuously on the financial market which consists of one risk-free asset and n risky assets (Black-Scholes market). We deal with the insurer's wealth path...

On capital allocation for stochastic arrangement increasing actuarial risks

Xiaoqing Pan, Xiaohu Li (2017)

Dependence Modeling

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This paper studies the increasing convex ordering of the optimal discounted capital allocations for stochastic arrangement increasing risks with stochastic arrangement decreasing occurrence times. The application to optimal allocation of policy limits is presented as an illustration as well.

Principal-agent approach to environmental improvements policies

Wojciech Szatzschneider, Teresa Kwiatkowska (2010)

Banach Center Publications

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Successful solution to any environmental problem implies working with Knightian uncertainty that explicitly deals with decision making under conditions of unstructured randomness. A 'wild' type of randomness that we will never discern due to its unstable properties makes the assignment of corresponding probabilities impossible. For that reason, the consideration of general economical factors within cost/benefit analysis must fail. So, instead of governmental intervention and a cup and...

Decomposition of large-scale stochastic optimal control problems

Kengy Barty, Pierre Carpentier, Pierre Girardeau (2010)

RAIRO - Operations Research

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In this paper, we present an Uzawa-based heuristic that is adapted to certain type of stochastic optimal control problems. More precisely, we consider dynamical systems that can be divided into small-scale subsystems linked through a static almost sure coupling constraint at each time step. This type of problem is common in production/portfolio management where subsystems are, for instance, power units, and one has to supply a stochastic power demand at each time step. We outline...

On the Bellman equation for asymptotics of utility from terminal wealth

Janusz Matkowski, Łukasz Stettner (2010)

Applicationes Mathematicae

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The asymptotics of utility from terminal wealth is studied. First, a finite horizon problem for any utility function is considered. To study a long run infinite horizon problem, a certain positive homogeneity (PH) assumption is imposed. It is then shown that assumption (PH) is practically satisfied only by power and logarithmic utility functions.