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On decision-making in possibility theory

Jiřina Vejnarová (2015)

Kybernetika

We present an alternative approach to decision-making in the framework of possibility theory, based on the idea of decision-making under uncertainty. We utilize the fact, that any possibility distribution can be viewed as an upper envelope of a set of probability distributions to which well-known minimax principle is applicable. Finally, we recall also an alternative to the minimax rule, so-called local minimax principle. Local minimax principle not only allows sequential construction of decision...

On European option pricing under partial information

Meng Wu, Jue Lu, Nan-jing Huang (2016)

Applications of Mathematics

We consider a European option pricing problem under a partial information market, i.e., only the security's price can be observed, the rate of return and the noise source in the market cannot be observed. To make the problem tractable, we focus on gap option which is a generalized form of the classical European option. By using the stochastic analysis and filtering technique, we derive a Black-Scholes formula for gap option pricing with dividends under partial information. Finally, we apply filtering...

On heuristic optimization.

Ciobanu, Camelia, Marin Gheorghe (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

On M -stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling

René Henrion, Werner Römisch (2007)

Applications of Mathematics

Modeling several competitive leaders and followers acting in an electricity market leads to coupled systems of mathematical programs with equilibrium constraints, called equilibrium problems with equilibrium constraints (EPECs). We consider a simplified model for competition in electricity markets under uncertainty of demand in an electricity network as a (stochastic) multi-leader-follower game. First order necessary conditions are developed for the corresponding stochastic EPEC based on a result...

On Nash theorem

Władysław Kulpa, Andrzej Szymański (2002)

Acta Universitatis Carolinae. Mathematica et Physica

On optimal credibility premiums in multiperiod insurance

W. Antoniak, M. Kałuszka (2014)

Applicationes Mathematicae

This paper focuses on the problem of optimal arrangement of a stream of premiums in a multiperiod credibility model. On the basis of a given claim history (screening) and some individual information unknown to the insurance company (signaling), we derive the optimal streams in the case when the coverage period is not necessarily fixed, e.g., because of lapses, renewals, deaths, total losses, etc.

On option pricing in the multidimensional Cox-Ross-Rubinstein model

Michał Motoczyński, Łukasz Stettner (1998)

Applicationes Mathematicae

Option pricing in the multidimensional case, i.e. when the contingent claim paid at maturity depends on a number of risky assets, is considered. It is assumed that the prices of the risky assets are in discrete time subject to binomial disturbances. Two approaches to option pricing are studied: geometric and analytic. A numerical example is also given.

On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve

Darija Marković, Dragan Jukić (2013)

International Journal of Applied Mathematics and Computer Science

The Bass model is one of the most well-known and widely used first-purchase diffusion models in marketing research. Estimation of its parameters has been approached in the literature by various techniques. In this paper, we consider the parameter estimation approach for the Bass model based on nonlinear weighted least squares fitting of its derivative known as the adoption curve. We show that it is possible that the least squares estimate does not exist. As a main result, two theorems on the existence...

On random processes as an implicit solution of equations

Petr Lachout (2017)

Kybernetika

Random processes with convenient properties are often employed to model observed data, particularly, coming from economy and finance. We will focus our interest in random processes given implicitly as a solution of a functional equation. For example, random processes AR, ARMA, ARCH, GARCH are belonging in this wide class. Their common feature can be expressed by requirement that stated random process together with incoming innovations must fulfill a functional equation. Functional dependence is...

On risk reserve under distribution constraints

Mariusz Michta (2000)

Discussiones Mathematicae Probability and Statistics

The purpose of this work is a study of the following insurance reserve model: R ( t ) = η + ∫ 0 t p ( s , R ( s ) ) d s + ∫ 0 t σ ( s , R ( s ) ) d W s - Z ( t ) , t ∈ [0,T], P(η ≥ c) ≥ 1-ϵ, ϵ ≥ 0. Under viability-type assumptions on a pair (p,σ) the estimation γ with the property: i n f 0 ≤ t ≤ T P R ( t ) ≥ c ≥ γ is considered.

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