Optimal Portfolio Selection with Consumption Under Stochastic Volatility PDF Download
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Author: 葛蕾
Publisher:
ISBN:
Category : Consumption (Economics)
Languages : en
Pages : 79
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Book Description
Author: 葛蕾
Publisher:
ISBN:
Category : Consumption (Economics)
Languages : en
Pages : 79
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Book Description
Author: Luis M. Viceira
Publisher:
ISBN:
Category : Assets (Accounting)
Languages : en
Pages : 48
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Book Description
Abstract: This paper analyzes optimal portfolio choice and consumption with stochastic volatility in incomplete markets. Using the Duffie-Epstein (1992) formulation of recursive utility in continuous time, it shows that the optimal portfolio demand for stocks under stochastic volatility varies strongly with the investor's coefficient of relative risk aversion, but only slightly with her elasticity of intertemporal substitution; by contrast, optimal consumption relative to wealth depends on both preference parameters. This paper also shows that stochastic variation in volatility produces an optimal intertemporal hedging demand for stocks which is negative when changes in volatility are instantaneously negatively correlated with excess stock returns and investors have coefficients of relative risk aversion larger than one. The absolute size of this demand increases with the size of this correlation, and also with the persistence of shocks to volatility. An application to the US stock market shows that empirically this correlation is negative and large, which implies a negative hedging demand for stocks. This application also shows that only low frequency shocks to volatility exhibit enough persistence to generate sizable hedging demands by long-term, risk averse investors. A comparative statics exercise shows that the size of hedging demands is considerably more sensitive to changes in persistence than to changes in correlation.
Author: Keqin Gong
Publisher:
ISBN: 9781303151552
Category :
Languages : en
Pages : 84
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Book Description
In this thesis, the classical Merton problem, a portfolio selection problem, is extended using multiscale volatility model which assumes that volatility of stock price depends on a fast scale process and a slow scale process. The Dynamic Programming Principle is used to establish the Hamilton-Jacobi-Bellman equation. An asymptotic method based on two small parameters from two scale factors, is applied in solving the equation to obtain an approximation of optimal trading strategy and value function, which is the expectation of utility of wealth in future. We also prove that when these two parameters are small, the error of our approximation of value function is small. Furthermore, we consider the counterparty risk in the portfolio selection problem, which means stock price has a jump at the default time and the stock is still tradable after default happens. In this scenario, an approximation of value function and optimal trading strategy is also derived and error of the approximation is estimated. Finally we use finite difference method to solve the problem and show how multiscale volatility model and counterparty default affect the results.
Author: George Yin
Publisher: Springer
ISBN: 3030254984
Category : Mathematics
Languages : en
Pages : 599
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Book Description
This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.
Author: Karan Thagunna
Publisher: LAP Lambert Academic Publishing
ISBN: 9783838353975
Category :
Languages : en
Pages : 112
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Book Description
In this dissertation, we consider a particular case of an optimal consumption and portfolio selection problem for an innitely lived investor whose consumption rate process is subject to downside constraint. We also suppose that the wealth dynamics is composed of three assets (i) riskless assets (ii) risky assets (iii) hedge assets. We consider the investor's wealth process, interpreted in the sense of the It DEGREESo integral.Our work aims to find the optimal policies which maximize the expected discount utility function.Furthermore, we obtain the optimal policies in an explicit form for the log utility function which is a special case of the general utility (CRRA) function, using the martingale method and applying the Legendre transform formula and the Feynman-kac formula. We derive some numerical results for the optimal policies and compare the results with the classical Merton's result evaluated for an innite horizon case.
Author: Pengyu Wei
Publisher:
ISBN:
Category :
Languages : en
Pages : 42
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Book Description
This paper analyzes the optimal consumption and portfolio choice problem for an ambiguity averse investor who has access to the stock and derivatives markets with recursive preferences. The stock process follows a stochastic volatility jump-diffusion model and the investor can have different levels of ambiguity about diffusion risks and the jump risk, respectively. We obtain an analytical solution which is exact when the investor has unit elasticity of intertemporal substitution of consumption, and approximate otherwise. We find that optimal exposures to diffusion risks and to the jump risk are significantly affected by the ambiguity aversion about the corresponding risk factors in the complete market. However, the optimal stock investment is insensitive to the ambiguity aversion about the jump risk in the incomplete market. We also find that considering ambiguity aversion with respect to diffusion risks and participating in the derivatives markets are essential to reduce the potential welfare loss, while the impact of ignoring the jump ambiguity is negligible.
Author: Ralf Korn
Publisher: World Scientific
ISBN: 9812385347
Category : Business & Economics
Languages : en
Pages : 352
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Book Description
The focus of the book is the construction of optimal investment strategies in a security market model where the prices follow diffusion processes. It begins by presenting the complete Black-Scholes type model and then moves on to incomplete models and models including constraints and transaction costs. The models and methods presented will include the stochastic control method of Merton, the martingale method of Cox-Huang and Karatzas et al., the log optimal method of Cover and Jamshidian, the value-preserving model of Hellwig etc.
Author: Tetsuya Adachi
Publisher:
ISBN:
Category :
Languages : en
Pages : 318
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Book Description
Author: Cuicui Luo
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Modeling time varying volatility and correlation in financial time series is an important element in derivative pricing, risk management and portfolio management. The main goal of this thesis is to investigate the performance of multivariate GARCH model in stochastic correlation forecast and apply theses techniques to develop a new model to enhance the dynamic portfolio performance in several context, including hedge fund portfolio construction.\\ First, we examine the performance of various univariate GARCH models and regime-switching stochastic volatility models in crude oil market. Then these univariate models discussed are extended to multivariate settings and the empirical evaluation provides evidence on the use of the orthogonal GARCH in correlation forecasting and risk management performance when an equally weighted portfolio is considered. \\ The recent financial turbulence exposed and raised serious concerns about the optimal portfolio selection problem in hedge funds. The dynamic portfolio construction performance of a broad set of multivariate stochastic volatility models is examined in a fund of hedge fund context. It provides further evidence on the use of the orthogonal GARCH in dynamic portfolio constructions and risk management. \\ Further in this work, a new portfolio optimization model is proposed in order to improve the dynamic portfolio performance. We enhance the safety-first model with standard deviation constraint and derive an analytic formula by filtering the returns with GH skewed t distribution and OGARCH. It is found that the proposed model outperforms the classical Mean-Variance model and Mean-CVAR model during financial crisis period for a fund of hedge fund.
Author: Andrea Buraschi
Publisher:
ISBN:
Category :
Languages : en
Pages : 58
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Book Description
We develop a new framework for intertemporal portfolio choice when the covariance matrix of returns is stochastic. An important contribution of this framework is that it allows to derive optimal portfolio implications for economies in which the degree of correlation across different industries, countries, and asset classes is time-varying and stochastic. In this setting, markets are incomplete and optimal portfolios include distinct hedging components against both stochastic volatility and correlation risk. The model gives rise to simple optimal portfolio solutions that are available in closed-form. We use these solutions to investigate, in several concrete applications, the properties of the optimal portfolios. We find that the hedging demand is typically four to five times larger than in univariate models and it includes an economically significant correlation hedging component, which tends to increase with the persistence of variance covariance shocks, the strength of leverage effects and the dimension of the investment opportunity set. These findings persist also in the discrete-time portfolio problem with short-selling or VaR constraints.
