Modern risk systems
Papers published in 2003

Companion sites: Russian version


  1. Novosyolov A.A. Inverse problems of risk theory and characteristic classes of distributions. Proceedings of the International Scientific School "Modelling and Analysis of Safety and Risk in Complex Systems", St.-Petersburg, August 2003, 445-450.

    Abstract. Building a model of individual preferences is a key for rational decision-making under uncertainty. Solution of this inverse problem may be simplified by proper using of available information. The present paper introduces the concept of characteristic class of a family of preferences, and presents usage of the concept for solving inverse problems. Characteristic classes for a number of families of preferences have been calculated.
    Key words: Decision-making, risk, individual preferences, risk measure, expected utility, distorted probability, combined functional, characteristic class.

    Download
  2. Novosyolov A.A. Risk aversion in the small with applications to portfolio analysis. Proceedings of the International Scientific School "Modelling and Analysis of Safety and Risk in Complex Systems", St.-Petersburg, August 2003, 261-265.

    Abstract. The concept of risk aversion was introduced by Pratt in 1964 for expected utility framework, and has attracted much attention as an important quantitative characteristic of individual attitude to risk. The current paper extends the concept to other decision-making frameworks, and presents exact quantitative results for distorted probability functional. Applications of the concept to portfolio analysis, and its relation with diversification concept are also being studied.
    Key words: Decision-making, risk, individual preferences, risk measure, risk aversion, expected utility, distorted probability, portfolio, diversification.

    Download
  3. Novosyolov A.A. Risk aversion in nonlinear decision-making models. Proceedings of the II All-Russian FAM conference, v. 1, Krasnoyarsk, 2003. (translated from Russian)

    Abstract. The risk aversion concept that was introduced by Pratt for expected utility model is being extended in the paper to nonlinear models of individual preferences. Quantitative measure of risk aversion has been proposed and calculated for distorted probability model. Illustrations are provided and a relation of risk aversion to diversification is pointed out.

    Download
  4. Novosyolov A.A. Characteristic Classes of Families of Risk Measures. Proceedings of the II All-Russian FAM conference, v. 1, Krasnoyarsk, 2003. (translated from Russian)

    Abstract. Decision-making under risk is usually implemented using a functional (risk measure) defined on a set of probability distributions and representing preference relation on the set. It is desirable to solve an inverse problem - constructing a risk measure representing given preference relation - on as narrow set of distributions as possible. The present paper introduces a concept of characteristic class of distributions for a family of risk measures, possessing the property that continuation of a risk measure from characteristic class to the whole set of distributions is unique within the family. Characteristic classes have been completely described for families of expected utility measures, distorted probability measures and combined functionals.

    Download
  5. Holton G.A., Novosyolov A.A. A numeric method for computing the distribution of a quadratic polynomial of a normal random vector. Proceedings of the II All-Russian FAM conference, v. 1, Krasnoyarsk, 2003. (translated from Russian)

    Abstract. The paper describes a numeric method for computing an improper integral, representing the distribution function of returns of a complex nonlinear financial portfolio.

    Download
  6. Novosyolov A.A. Combined functionals as risk measures. Proceedings of the Bowles Symposium, Atlanta, April 10-11, 2003.

    Abstract. Risk measures are widely used in insurance pricing, portfolio selection, and in decision-making in general. Two prevalent classes of risk measures are expected utility (a dollar transform), and distorted probability (a probability transform). Both approaches exhibit properties which are not supported by empirical evidence on decision-making under risk. We propose a combined functional (dollar and probability transform) which may combine advantages of both approaches. The present paper develops representation theorems and axiomatic descriptions, presents applications to decision-making under risk, premium calculation, and portfolio selection; and includes numeric and graphical illustrations.
    Key words: risk measure, expected utility, distorted probability, combined functional, premium calculation, portfolio selection, decision-making.

    Download
    paper, presentation
  7. Novosyolov A.A. Using indifference curves for decision-making under risk. In: Contemporary economics; problems and solutions. Krasnoyarsk, KrasGU, 2003. (translated from Russian)

    Abstract. The paper is devoted to using information on individual investor preferences, in particular - indifference curves - in portfolio analysis problems and decision-making under risk. It has been shown that ignoring the information in classical portfolio methods may cause unacceptable solutions. A method of using information on individual preferences in decision-making problems is being proposed. Numeric examples are also given.

    (To appear soon).
  8. Kondratenko Yu.V., Novosyolov A.A. Mathematical models of ecological catastrophes: environment contamination. Vestnik of the Krasnoyarsk state university, 1 (2003), p. 97-101 (in Russian).

    Abstract. The paper is devoted to a model of environment contamination which is a development of a Khlebopros model. As in the original model, the environment self-cleaning characteristic is assumed a known nonlinear function, while the contaminating is described by a random process. Dynamics of contamination process and its steady states have been studied, numeric examples are provided.

    Unavailable for downloading.

Home Basics Lectures Papers Download Links Contact
Copyright © 2000-2017, A.Novosyolov Last changed at 22.07.2015