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1

Choosing a lawyer as a special case of self-insurance-cum-protection

Dudziński P.

Mathematica Applicanda

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2013

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Vol. 41, No. 2

171--184

EN

We consider the problem of choosing a lawyer as a particular case of selfinsurance- cum-protection (SICP) when the lawyer’s costs are covered in the case of victory. This problem was introduced by Sevi and Yafil (2005) in the context of selfprotection (SP), with the assumption that the size of a loss does not depend on the level of effort (expenditure on a lawyer). In this paper we drop that assumption and our model considers the possibility that both the loss and probability of incurring a loss depend on effort. We compare the optimal effort in our case with the standard one and prove that, according to the modified model of SICP, repayment is a good incentive to invest more. We also show that, unlike in the standard cases of SP and SICP, the level of effort is monotone in the level of risk aversion. We prove that, according to our model, decreasing absolute risk aversion (DARA) implies that a lawyer’s service is a normal good, which is intuitive. We show that for a certain type of increase in risk aversion, the reimbursement effect is stronger than the risk aversion effect. For other changes in risk aversion, there is a probability threshold such that if the probability of a loss is below that level, then the risk-aversion effect prevails. For higher initial probabilities, the reimbursement effect is stronger.

PL

Analizujemy decyzje o wyborze prawnika jako szczególnym przypadku samoubezpieczenia z ochroną, gdy koszt prawnika zostanie spłacony w przypadku wygrania procesu. Problem został wprowadzony przez Sevi i Yafil(2005) w kontekście obrony, która wymaga założenia, że wielkość strat nie zależy od wysiłku (poziom wydatków na adwokata ).

2

Risk aversion in maintenance

Baker R.D.

Eksploatacja i Niezawodność

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2006

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nr 2

14-16

EN

The concept of risk averse maintenance is introduced. It is formulated in terms of seeking to minimize a disutility rather than a cost per unit time. A general formalism is given, followed by an example, the application to age-based replacement. The problem of overmaintenance caused by undue risk aversion on the part of engineers is briefly discussed.

3

Multiple criteria optimization and decisions under risk

Ogryczak W.

Control and Cybernetics

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2002

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Vol. 31, no 4

975-1003

EN

The mathematical background of multiple criteria optimization (MCO) is closely related to the theory of decisions under uncertainty. Most of the classical solution concepts commonly used in the MCO methodology have their origins in some approaches to handling uncertainty in decision analysis. Nevertheless, the MCO as a separate discipline has developed several advanced tools of interactive analysis leading to effective decision support techniques with successful applications. Progress made in the MCO tools raises a question of possible feedback to the decision making under risk. The paper shows how decisions under risk, and specifically the risk aversion preferences, can be modeled within the MCO methodology. This provides a methodological basis allowing for taking advantage of the interactive multiple criteria techniques for decision support under risk.

PL

Podstawy matematyczne optymalizacji wielokryterialnej są blisko związane z teorią podejmowania decyzji w warunkach ryzyka. Większość klasycznych koncepcji rozwiązań zazwyczaj wykorzystywanych w metodach optymalizacji wielokryterialnej pochodzi z pewnych podejść uwzględniania niepewności w analizie decyzji. Jednakże, należy podkreślić, że optymalizacja wielokryterialna, jako niezależna dyscyplina, rozwinęła szereg zaawansowanych narzędzi analizy interaktywnej, prowadzących do efektywnych technik wspomagania decyzji, znajdujących rzeczywiste zastosowania. Postęp, jaki się dokonał w zakresie narzędzi wielokryterialnego podejmowania decyzji, stawia pytanie o ewentualne sprzężenie zwrotne w kierunku podejmowania decyzji w warunkach ryzyka. W artykule pokazano, jak decyzje z ryzykiem, a szczególnie preferencje co do unikania ryzyka, mogą być modelowane przy użyciu metodyki optymalizacji wielokryterialnej. W ten sposób stworzono podstawę metodyczną pozwalającą korzystać z interaktywnych technik wielokryterialnych we wspomaganiu decyzji z ryzykiem.

4

Valuation of catastrophe bonds

Kulikowski R., Jakubowski A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2000

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Vol. 48, nr 2

182-211

EN

A new approach to valuation of bonds under the default risk conditions, based on the concept of the investors' two-factor utility function is proposed. The first factor describes the expected average return from the risky investments, while the second - the worst case return. As a class of risky securities the so called catastrophe bonds are considered. It is assumed that depending on the structure of the security contract, the investor who buys the bond issued by a local authority governing the risky region - will lose his interest payments and/or the principal value, if a catastrophic event occurs. In the paper, the problem of pricing the catastrophe bonds is thoroughly analysed. The answer to one main question is given. It is how much of the default risk premium should be paid to an investor in order to compensate for risk, attached to the consequences of a catastrophe which can occur wit h same estimated probability. For the purpose of the valuation procedure, the new notions of the security safety level, the safety index, as well as a two rules decision model are successively introduced. The subjective scale as a measure of the degree of individuals' risk aversion is proposed. The idea of objective and subjective risk components is investigated. The new methodology proposed is illustrated by a series of computational examples. The results obtained, in the assumed conditions closed to a real life practice, are widely interpreted and discussed.

5

Two factors utility approach

Kulikowski R.

Control and Cybernetics

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1998

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Vol. 27, no 3

417-428

EN

This paper deals with optimization of portfolios composed of securities (equities). The drawbacks of existing methodologies, based on a single factor utility function, are indicated. The two-factor utility function introduced takes into account the expected excess return and expected worst case return (both in monetary units). Assuming that utility is "risk averse" and "constant returns to scale", a theorem on existence of optimum strategy of investments is proven. The optimum strategy is derived in an explicit form. A numerical example is also given.

6

Portfolio optimization - two rules approach

Kulikowski R.

Control and Cybernetics

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1998

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Vol. 27, no 3

429-446

EN

The new approach to the portfolio optimization, based on the concept of two-factor utility function, is proposed. The first factor describes the expected average profit, while the second - the worse case profit. Then, two rules enabling one to compose an optimum portfolio are formulated. The first rule determines the level of acceptance for all assets with given risk/return ratio. The second rule enables one to allocate the investment fund among all the accepted assets. The methodology proposed does not require to specify the individual utility function in an explicit form. It can be used to optimize portfolios composed of equities as well as bond and other securities, using a passive or - active management strategy.