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Your search keyword '"incomplete financial market"' showing total 3 results
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3 results on '"incomplete financial market"'

1. A discrete-time model that weakly converges to a continuous-time geometric Brownian motion with Markov switching drift rate.

Author

Golomoziy, Vitaliy, Mishura, Yuliya, Kladivko, Kamil, Melnikov, Alexander, Martinucci, Barbara, and Manstavicius, Martynas

Subjects
INCOMPLETE markets, MARKOV processes, GEOMETRIC topology, FINANCIAL markets, MARTINGALES (Mathematics)
Abstract

This research is devoted to studying a geometric Brownian motion with drift switching driven by a 2 χ 2 Markov chain. A discrete-time multiplicative approximation scheme was developed, and its convergence in Skorokhod topology to the continuous-time geometric Brownian motion with switching has been proved. Furthermore, in a financial market where the discounted asset price follows a geometric Brownian motion with drift switching, market incompleteness was established, and multiple equivalent martingale measures were constructed. [ABSTRACT FROM AUTHOR]

Published
2024
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2. A discrete-time model that weakly converges to a continuous-time geometric Brownian motion with Markov switching drift rate

Author

Vitaliy Golomoziy, Yuliya Mishura, and Kamil Kladívko

Subjects
geometric Brownian motion, Markov switching, discrete-time multiplicative approximation, equivalent martingale measure, incomplete financial market, Applied mathematics. Quantitative methods, T57-57.97, Probabilities. Mathematical statistics, QA273-280
Abstract

This research is devoted to studying a geometric Brownian motion with drift switching driven by a 2 × 2 Markov chain. A discrete-time multiplicative approximation scheme was developed, and its convergence in Skorokhod topology to the continuous-time geometric Brownian motion with switching has been proved. Furthermore, in a financial market where the discounted asset price follows a geometric Brownian motion with drift switching, market incompleteness was established, and multiple equivalent martingale measures were constructed.

Published
2024
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3. Financial Economics

Author

Knut K. Aase

Subjects
representative agent, pareto optimality, Financial economics, Economics, Representative agent, Competitive equilibrium, incomplete financial market, competitive equilibrium, marketed subspace
Abstract

We consider a one period (two time points-) model of efficient risk sharing, when the risk of possible sharing rules are constrained to be linear. This can be interpreted as a model of a market for common stocks. Here we study the properties of a competitive equilibrium in an incomplete market. The lack of Pareto optimality is then the typical case. We do characterize, however, the situations where the competitive financial equilibrium is also Pareto optimal, and illustrate by examples. Since the marketed subspace M is a closed, linear subspace of L2, we employ Hilbert space techniques in finding the first order conditions. We conclude with a discussion of the different features of idiosyncratic risks in insurance, and risks in financial markets, where a common ground is suggested.

Published
2014
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