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  1. 3 Applicationes Mathematicae

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  1. 3 Delong Ł.

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  1. 2 2012

  2. 1 2005

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Exponential utility optimization, indifference pricing and hedging for a payment process

100%
Delong Ł.
Applicationes Mathematicae
|
2012
|
tom 39
|
nr 2
211-229
EN
We deal with pricing and hedging for a payment process. We investigate a Black-Scholes financial market with stochastic coefficients and a stream of liabilities with claims occurring at random times, continuously over the duration of the contract and at the terminal time. The random times of the claims are generated by a random measure with a stochastic intensity of jumps. The claims are written on the asset traded in the financial market and on the non-tradeable source of risk driven by the random measure. Our framework allows us to consider very general streams of liabilities which may arise in financial and insurance applications. We solve the exponential utility optimization problem for our payment process and we derive the indifference price and hedging strategy. We apply backward stochastic differential equations.
2
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Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance

100%
Delong Ł.
Applicationes Mathematicae
|
2012
|
tom 39
|
nr 4
463-488
EN
We investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in insurance and finance in an attempt to find an investment strategy and an investment portfolio which should replicate a liability or meet a target depending on the strategy applied or the past values of the portfolio. In this setting, a managed investment portfolio serves simultaneously as the underlying security on which the liability/target is contingent and as a replicating portfolio for that liability/target. This is usually the case of capital-protected investments and performance-linked pay-offs. We give examples of pricing, hedging and portfolio management problems (asset-liability management problems) which could be investigated in the framework of time-delayed BSDEs. We focus on participating contracts and variable annuities. We believe that time-delayed BSDEs could offer a tool for studying investment life insurance contracts from a new and desirable perspective.
3
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Optimal investment strategy for a non-life insurance company: quadratic loss

100%
Delong Ł.
Applicationes Mathematicae
|
2005
|
tom 32
|
nr 3
263-277
EN
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 dependent disutility optimization problem and apply a quadratic loss function which penalizes deviations below a reserve for outstanding liabilities as well as above a given upper barrier. An optimal investment strategy is derived using stochastic control theory in the absence of constraints on control variables. Some properties of the strategy and the behaviour of the insurer's wealth under the optimal control are investigated. The set up of our model is more general, as it can also be used in non-life loss reserving problems.
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