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Author: Julian Hölzermann Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This paper studies dynamic asset allocation with interest rate risk and several sources of ambiguity. The market consists of a risk-free asset, a zero-coupon bond (both determined by a Vasicek model), and a stock. There is ambiguity about the risk premia, the volatilities, and the correlation. The investor's preferences display both risk aversion and ambiguity aversion. The optimal investment problem can be solved in closed-form under typical market conditions. The solution shows that the investor does not hedge ambiguity but only risk, while the ambiguity only affects the speculative motives of the investor. An implementation of the optimal investment strategy shows the impact of the different sources of ambiguity. Ambiguity aversion helps to tame the highly leveraged portfolios neglecting ambiguity and leads to strategies that are more in line with popular investment advice. The solution method for the optimal investment problem is based on an extension of the martingale optimality principle.
Author: Julian Hölzermann Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This paper studies dynamic asset allocation with interest rate risk and several sources of ambiguity. The market consists of a risk-free asset, a zero-coupon bond (both determined by a Vasicek model), and a stock. There is ambiguity about the risk premia, the volatilities, and the correlation. The investor's preferences display both risk aversion and ambiguity aversion. The optimal investment problem can be solved in closed-form under typical market conditions. The solution shows that the investor does not hedge ambiguity but only risk, while the ambiguity only affects the speculative motives of the investor. An implementation of the optimal investment strategy shows the impact of the different sources of ambiguity. Ambiguity aversion helps to tame the highly leveraged portfolios neglecting ambiguity and leads to strategies that are more in line with popular investment advice. The solution method for the optimal investment problem is based on an extension of the martingale optimality principle.
Author: Ralf Korn Publisher: World Scientific ISBN: 9812385347 Category : Business & Economics Languages : en Pages : 352
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: Qian Lin Publisher: ISBN: Category : Languages : en Pages :
Book Description
We consider optimal consumption and portfolio choice in the presence of Knightian uncertainty in continuous-time. We embed the problem into the new framework of stochastic calculus for such settings, dealing in particular with the issue of non-equivalent multiple priors. We solve the problem completely by identifying the worst-case measure. Our setup also allows to consider interest rate uncertainty; we show that under some robust parameter constellations, the investor optimally puts all his wealth into the asset market, and does not save or borrow at all.
Author: Claus Munk Publisher: ISBN: Category : Languages : en Pages : 63
Book Description
We investigate the optimal investment and consumption choice of individual investors with uncertain future labor income operating in a financial market with stochastic interest rates. Since the present value of the individual's future income is a main determinant of the optimal behavior and this present value depends heavily on the interest rate dynamics, the joint stochastics of income and interest rates will have consequences beyond the separate effects of stochastic income and stochastic interest rates. We study both the case where income risk is spanned and there are no portfolio constraints and the case with non-spanned income risk and a constraint ruling out borrowing against future income. For the spanned, unconstrained problem we study a special case in which we obtain closed-form expressions for the optimal policies. For the unspanned, constrained problem we implement a numerical solution technique and compare the solutions to the spanned, unconstrained problem. We also allow for typical life-cycle variations in labor income.
Author: Anne Balter Publisher: ISBN: Category : Languages : en Pages : 35
Book Description
We study portfolio choice in a Black-Scholes world under drift uncertainty. Preferences towards risk and ambiguity are modeled using the smooth ambiguity approach under a double power utility assumption and a normal distribution assumption on the unknown drift. Optimal investment in this setting is time-inconsistent: While utility is maximized by a precommitment strategy resembling the classical Merton solution, the investor's future selves prefer to constantly increase the riskiness of the strategy. In contrast, the optimal dynamically consistent investment strategy accounts for variations in the perceived severity of drift uncertainty, thus increasing the riskiness of the strategy gradually over time. We provide a detailed comparative analysis of the mechanics and interplay of ambiguity, myopia and optimal decisions in this setting. We show that an investor who pre-commits will regret that decision from some time point onwards, wishing that she had followed the dynamically consistent strategy. This “point of regret” always lies near the middle of the investment horizon.
Author: Julian Hölzermann
Author: Julian Hölzermann
Author: Tina Engler
Author: Claus Munk
Author: Ralf Korn
Author: Claus Munk
Author: Qian Lin
Author: Claus Munk
Author: Claus Munk
Author: Anne Balter
Author: Thomas Knispel