Modern risk systems

Companion sites: Russian version

Abstracts and full texts of selected old lectures, which were delivered to students at Krasnoyarsk universities, are presented here. Russian versions of these lectures are also available.

  1. Relations (KSU).
    The concept of relation on a set is introduced. Equivalence, order and preference relations are considered and interrelations between them are established. (Uploaded - 2/5/2002)
  2. Correspondences (KSU).
    Concepts of correspondence, polar and component are studies. Interrelations of these concepts with those of function and relation is established. (Uploaded - 2/5/2002)
  3. Basic concepts of risk theory (KSU).
    Risk theory is described as decision-making under probabilistic uncertainty. Basic concepts are introduced, the main problem is stated, branches of the theory are outlined, and usual applications are presented. (Uploaded - 1/4/2002)
  4. Distorted probability measure (KSU).
    A risk measure called distorted probability measure is described. Properties of the measure are discussed as well as methods of its calculation and statistical estimation. (Uploaded - 2/6/2002)
  5. Market insurance premium (SibSTU).
    A method of insurance premium calculation that takes market demand into account is being considered. The method is maximization cover probability given demand function. Sensitivity of cover probability to premium in a neighborhood of current premium is also studied.
  6. Investment portfolio selection (KSU).
    A problem of portfolio selection is considered as a problem of optimization in Rn. Special cases are also treated: minimization of variance of portfolio return, Markowitz problem, maximization of expected utility. Interrelations among these models are established. Special attention is being paid to investor's attitude to risk in these models. (Uploaded - 1/27/2002)
  7. Uniform distribution on a standard simplex in Rn (KSU).
    In portfolio selection problems it is often necessary to solve optimization problems on a standard simplex in Rn by Monte Carlo methods. To implement this one needs a sample from uniform distribution on the standard simplex. In this lecture a method of simulation this distribution is presented. (Uploaded - 04/25/2002)
  8. Simple insurance portfolios (SibSTU).
    Basic approaches to calculation non-life insurance premium are presented. (Uploaded - 3/7/2002)
  9. Monte Carlo method (KSU).
    Monte Carlo method is presented as well as its applications to risk theory problems. (To appear)

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