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# Asset pricing and portfolio optimization under regime switching models

thesis
posted on 2022-03-29, 00:00 authored by Yang Shen
Recently, there has been a considerable interest in applications of regime-switching models in various aspects of finance and insurance. One of the main features of these models is that some model parameters are modulated by a finite-state Markov chain. This makes regime-switching models very useful to describe structural changes in macro-economic conditions, periodical fluctuations in business cycles and sudden transitions in market modes. In this thesis, a continuous-time, finite-state, observable Markov chain is adopted to model the regime switches. Our regime-switching models are a set of diffusion models, jump-diffusion models or Levy models coupled by the underlying Markov chain. Under this modeling set up, the financial market is incomplete. So asset pricing and portfolio optimization problems are more involved. Roughly speaking, this thesis can be divided into two parts. The first part is devoted to asset pricing problems under regime-switching models. Due to the market incompleteness, the equivalent martingale measure is not unique. Therefore, we either choose a particular equivalent martingale measure using the Esscher transform or start directly from a risk-neutral measure. We present analytical pricing formulae for European options and variance swaps in Chapters 2 and 3, respectively. Numerical and empirical implementations of these formulae show that the regime-switching effect is material for asset pricing problems. In the second part of this thesis, we apply the stochastic optimal control theory to discuss portfolio optimization problems under regime-switching models. In Chapter 4, we use the dynamic programming principle approach to solve a mean-variance portfolio selection problem with uncertain investment horizon. Explicit expressions of the efficient portfolio and the efficient frontier are obtained. In Chapter 5, the stochastic optimal control theory for portfolio optimization problems is borrowed to investigate an fundamental issue in asset pricing problems, i.e. the selection of equivalent martingale measures. We derive and compare equivalent martingale measures selected by three different approaches, that is, the stochastic differential game approach, the Esscher transformation approach and the general equilibrium approach.

## History

1. Introduction -- 2. Option valuation under a double regime-switching model -- 3. Pricing variance swaps under a stochastic interest rate and volatility model with regime switching -- 4. Mean-variance portfolio selection with uncertain investment horizon under a regime-switching jump-diffusion model -- 5. Stochastic differential game, Esscher transform and general equilibrium under a Markovian regime-switching Lévy model -- 6. Conclusion.

## Notes

Bibliography: pages 145-155 Theoretical thesis.

## Awarding Institution

Macquarie University

Thesis PhD

## Degree

PhD, Macquarie University, Faculty of Business and Economics, Department of Applied Finance and Actuarial Studies

## Department, Centre or School

Department of Applied Finance and Actuarial Studies

2014

Tak Kuen Siu

Xian Zhou

English

## Extent

1 online resource (ix, 157 pages) colour illustrations

## Former Identifiers

mq:71843 http://hdl.handle.net/1959.14/1278674

## Exports

figshare. credit for all your research.