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Author: Claus Munk Publisher: ISBN: Category : Languages : en Pages : 44
Book Description
We characterize the solution to the consumption and investment problem of a time-additive power utility investor in a continuous-time dynamically complete market with stochastic changes in the opportunity set. It is demonstrated that under stochastic interest rates the investor optimally hedges against changes in the term structure of interest rates by investing in a coupon bond, or portfolio of bonds, with a payment schedule that matches the forward-expected (i.e. certainty equivalent) consumption pattern. This is of conceptual importance since the hedge portfolio only depends on the specic term structure dynamics through the consequences for the optimal consumption pattern. We consider two explicit examples where the term structure dynamics are given by the Vasicek model and a three factor non-Markovian Heath-Jarrow-Morton model.
Author: Claus Munk Publisher: ISBN: Category : Languages : en Pages : 44
Book Description
We characterize the solution to the consumption and investment problem of a time-additive power utility investor in a continuous-time dynamically complete market with stochastic changes in the opportunity set. It is demonstrated that under stochastic interest rates the investor optimally hedges against changes in the term structure of interest rates by investing in a coupon bond, or portfolio of bonds, with a payment schedule that matches the forward-expected (i.e. certainty equivalent) consumption pattern. This is of conceptual importance since the hedge portfolio only depends on the specic term structure dynamics through the consequences for the optimal consumption pattern. We consider two explicit examples where the term structure dynamics are given by the Vasicek model and a three factor non-Markovian Heath-Jarrow-Morton model.
Author: Daniel Synowiec Publisher: LAP Lambert Academic Publishing ISBN: 9783659182587 Category : Languages : en Pages : 96
Book Description
Optimal portfolio selection problems have been investigated since the late 1960's. Most of them are concerned with investment in a savings account on a constant rate and a finite number of stocks. Then the explicit solution is given. Over the last few years, a problem of an investment in the bond market, with an interest rate changing in time but without possibility of consumption, has been considered. In this book, it is considered an investor problem with an interest rate given by a stochastic differential equation and with possibility of consumption as well as investing money both in savings account and in zero-coupon bonds. There are given formulae for both optimal portfolio and optimal consumption strategy. On the other hand, an investor problem in discrete time case with forward rate given by Markov chain is analyzed. Theoretical results are illustrated with interesting examples. The book should be useful to all interested in applications of stochastic control theory, or anyone else whose area of interest is financial mathematics.
Author: Claus Munk Publisher: ISBN: Category : Languages : en Pages : 43
Book Description
We study the dynamic consumption and portfolio choice of an investor who has habit formation in preferences and access to a complete financial market. For general, possibly non-Markov, dynamics of market prices, we provide an exact characterization of the optimal behavior in terms of two relatively simple and intuitively interpretable stochastic processes. We study in more detail the optimal strategies in two concrete examples of time-varying investment opportunities. Firstly, we derive a closed-form solution of the optimal consumption and portfolio choice with mean-reverting stock returns. Secondly, with Cox-Ingersoll-Ross interest rate dynamics we can express the optimal strategies in terms of the solution to a partial differential equation, which has an explicit solution for time-additive preferences, but not with habit formation. Our numerical examples show that, while hedging demands for various assets are affected differently by habit persistence, the main effect on relative asset allocations stems from the fact that some assets (bonds and cash) are better investment objects than others (stocks) when it comes to ensuring that future consumption will not fall below the habit level. The implications of habit persistence in models with labor income are also addressed.
Author: Paolo Guasoni Publisher: ISBN: Category : Languages : en Pages : 26
Book Description
This paper investigates the optimal investment and consumption problem in a continuous-time financial market for investors with power utility on consumption, who face partially hedgeable interest rate risk. With no analytical solution to the optimal strategies, closed-form approximate strategies are derived by solving the same optimization problem in two fictitious complete markets. The approximate solution helps verify the existence and the optimality of the solution to the original optimization problem and provides bounds of the optimal consumption strategy and the approximation error, both in closed form. As the interest rate increases, if the investor's risk aversion is greater than one, the wealth effect dominates the substitution effect, and consumption increases. If risk aversion is less than one, then the substitution effect dominates, and the investor consumes less.
Author: Anders Damgaard Publisher: ISBN: Category : Languages : en Pages : 44
Book Description
We study the consumption and investment choice of an agent in a continuous-time economy with a riskless asset, several risky financial assets, and two consumption goods, namely a perishable and a durable good with an uncertain price evolution. Assuming lognormal prices and a multiplicatively separable, isoelastic utility function, we provide an explicit Merton-type solution for the optimal strategies for the case where the durable (and all other assets) can be traded without transaction costs. For the case where the durable good is indivisible, in the sense that durable trades imply transaction costs proportional to the value of the current durable holdings, we show analytically that the optimal durable trading strategy is characterized by three constants underline{z} lt; z* lt; overline{z}. As long as the ratio z of the total current wealth to the value of current durable holdings of the investor is in ( underline{z}, overline{z}), it is optimal not to trade the durable. At the boundaries of this interval it is optimal to trade the durable to attain z = z*. The model is used to examine the optimal substitution between perishable and durable consumption and the importance of the durable price uncertainty and the correlation between the price of the durable good and financial asset prices.
Author: Holger Kraft Publisher: ISBN: Category : Languages : en Pages : 63
Book Description
We provide explicit solutions to life-cycle utility maximization problems involving dynamic decisions on investments in stocks and bonds, consumption of perishable goods, and the rental and the ownership of residential real estate. House prices, stock prices, interest rates, and the labor income of the decision-maker follow correlated stochastic processes. The explicit consumption and investment strategies are simple and intuitive and are thoroughly discussed and illustrated in the paper. A calibrated version of the model exhibits many interesting and realistic features. For example, due to a positive correlation between house prices and labor income, young individuals want little (or even negative) exposure to house price risk and tend to rent their home. Later in life, when human wealth declines, the desired housing investment increases and will eventually reach and exceed the desired housing consumption, suggesting that the individual should buy his home--and buy either additional housing units (for renting out) or house price linked financial assets. In the final years, preferences shift back to home rental. While our model involves continuous adjustments of the consumption of housing services and the exposure of wealth to house price risk, we demonstrate that the derived strategies are still useful if the housing positions are only reset infrequently. Our results suggest that markets for REITs or other financial contracts linked to house prices will lead to non-negligible improvements of welfare.
Author: W. T. Ziemba Publisher: World Scientific ISBN: 9812773657 Category : Business & Economics Languages : en Pages : 756
Book Description
A reprint of one of the classic volumes on portfolio theory and investment, this book has been used by the leading professors at universities such as Stanford, Berkeley, and Carnegie-Mellon. It contains five parts, each with a review of the literature and about 150 pages of computational and review exercises and further in-depth, challenging problems. Frequently referenced and highly usable, the material remains as fresh and relevant for a portfolio theory course as ever. Sample Chapter(s). Chapter 1: Expected Utility Theory (373 KB). Contents: Mathematical Tools: Expected Utility Theory; Convexity and the Kuhn-Tucker Conditions; Dynamic Programming; Qualitative Economic Results: Stochastic Dominance; Measures of Risk Aversion; Separation Theorems; Static Portfolio Selection Models: Mean-Variance and Safety First Approaches and Their Extensions; Existence and Diversification of Optimal Portfolio Policies: Effects of Taxes on Risk Taking; Dynamic Models Reducible to Static Models: Models That Have a Single Decision Point; Risk Aversion over Time Implies Static Risk Aversion; Myopic Portfolio Policies; Dynamic Models: Two-Period Consumption Models and Portfolio Revision; Models of Optimal Capital Accumulation and Portfolio Selection; Models of Option Strategy; The Capital Growth Criterion and Continuous-Time Models. Readership: Postdoctoral and graduate students, researchers, academics, and professionals interested in portfolio theory and stochastic optimization.
Author: Claus Munk
Author: Claus Munk
Author: Claus Munk
Author: Tina Engler
Author: Daniel Synowiec
Author: Claus Munk
Author: Paolo Guasoni
Author: Claus Munk
Author: Anders Damgaard
Author: Holger Kraft
Author: W. T. Ziemba