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1

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.

2

Multiobjective duality for the Markowitz portfolio optimization problem

Wanka G.

Control and Cybernetics

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1999

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Vol. 28, no 4

691-702

EN

The classical Markowitz approach to portfolio selection leads to a biobjective optimization problem where the objectives are the expected return and the variance of a portfolio. In this paper a biobjective dual optimization problem to the Markowitz portfolio optimization problem is introduced and analyzed. For the Markowitz problem and its dual, weak and strong vector duality assertions are derived. The optimality conditions are also verified.

3

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.

4

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.