Optimal Long Term Investment Under Model Ambiguity PDF Download

Author: Thomas Knispel
Publisher:
ISBN:
Category :
Languages : en
Pages : 169

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Author: Anne Balter
Publisher:
ISBN:
Category :
Languages : en
Pages : 35

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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: Thomas Dangl
Publisher:
ISBN:
Category :
Languages : en
Pages : 51

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We study the implications of predictability on the optimal asset allocation of ambiguity-averse long-term investors and analyze the term structure of the multivariate risk-return trade-off considering parameter uncertainty. We calibrate the model to real returns of US stocks, long-term bonds, cash, real estate, and gold using the term spread and the dividend-price ratio as additional predictive variables, and we show that over long horizons the optimal asset allocation is significantly influenced by the covariance structure induced by estimation errors. The ambiguity-averse long-term investor optimally tilts her portfolio toward a seemingly inefficient portfolio, which shows maximum robustness against estimation errors.

Author: David Schröder
Publisher:
ISBN:
Category :
Languages : en
Pages : 40

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Recent literature on optimal investment has stressed the difference between the impact of risk and the impact of ambiguity - also called Knightian uncertainty - on investors' decisions. In this paper, we show that a decision maker's attitude towards ambiguity is similarly crucial for investment decisions. We capture the investor's individual ambiguity attitude by applying alpha-MEU preferences to a standard investment problem. We show that the presence of ambiguity often leads to an increase in the subjective project value, and entrepreneurs are more eager to invest. Thereby, our investment model helps to explain differences in investment behavior in situations which are objectively identical.

Author: Julian Hölzermann
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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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: Sigrid Källblad
Publisher:
ISBN:
Category :
Languages : en
Pages : 41

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We combine forward investment performance processes and ambiguity averse portfolio selection. We introduce the notion of robust forward criteria which addresses the issues of ambiguity in model specification and in preferences and investment horizon specification. It describes the evolution of time-consistent ambiguity averse preferences. We first focus on establishing dual characterizations of the robust forward criteria. This offers various advantages as the dual problem amounts to a search for an infimum whereas the primal problem features a saddle-point. Our approach is based on ideas developed in Schied (2007) and Zitkovic (2009). We then study in detail non-volatile criteria. In particular, we solve explicitly the example of an investor who starts with a logarithmic utility and applies a quadratic penalty function. The investor builds a dynamical estimate of the market price of risk and updates her stochastic utility in accordance with the so-perceived elapsed market opportunities. We show that this leads to a time-consistent optimal investment policy given by a fractional Kelly strategy associated with the investor's estimate. The leverage is proportional to the investor's confidence in her estimate.

Author: Bong-Gyu Jang
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Integrating a Value-at-Risk constraint on a fund manager's wealth and ambiguity, we present a model of optimal portfolio choice for a fund manager who allocates her wealth between risky and riskless assets. When a fund manager controls asset composition, her reactions di er with respect to an increase in only risk aversion and only ambiguity aversion. When the sum of coe cients of risk aversion and ambiguity aversion is fixed, the effect of risk aversion on risky investment dominates the effect of ambiguity aversion in that stock holdings are dramatically smaller in the absence of ambiguity aversion than in its presence.

Author: L. C. G. Rogers
Publisher: Springer Science & Business Media
ISBN: 3642352022
Category : Mathematics
Languages : en
Pages : 163

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Book Description
Readers of this book will learn how to solve a wide range of optimal investment problems arising in finance and economics. Starting from the fundamental Merton problem, many variants are presented and solved, often using numerical techniques that the book also covers. The final chapter assesses the relevance of many of the models in common use when applied to data.

Author: Robert K. Dixit
Publisher: Princeton University Press
ISBN: 1400830176
Category : Business & Economics
Languages : en
Pages : 484

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Book Description
How should firms decide whether and when to invest in new capital equipment, additions to their workforce, or the development of new products? Why have traditional economic models of investment failed to explain the behavior of investment spending in the United States and other countries? In this book, Avinash Dixit and Robert Pindyck provide the first detailed exposition of a new theoretical approach to the capital investment decisions of firms, stressing the irreversibility of most investment decisions, and the ongoing uncertainty of the economic environment in which these decisions are made. In so doing, they answer important questions about investment decisions and the behavior of investment spending. This new approach to investment recognizes the option value of waiting for better (but never complete) information. It exploits an analogy with the theory of options in financial markets, which permits a much richer dynamic framework than was possible with the traditional theory of investment. The authors present the new theory in a clear and systematic way, and consolidate, synthesize, and extend the various strands of research that have come out of the theory. Their book shows the importance of the theory for understanding investment behavior of firms; develops the implications of this theory for industry dynamics and for government policy concerning investment; and shows how the theory can be applied to specific industries and to a wide variety of business problems.

Author: Yuhong Xu
Publisher:
ISBN:
Category :
Languages : en
Pages : 22

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In this paper I investigate financial markets with drift and volatility uncertainties. Appropriate definitions of arbitrage for super and sub-hedging strategies are presented such that the super and sub-hedging prices are reasonable. Especially the condition of arbitrage for sub-hedging strategy fills the gap of the theory of arbitrage under model uncertainty. The Profit&Loss (P&L for short) of super(sub)-hedging is derived to be in fact the penalty term K with finite-variance arising in the super(sub)-hedging strategy. The ask-bid spread is hence an accumulation of the superhedging P&L and the subhedging P&L.Asset allocation under constant absolute risk aversion (CARA) utility is investigated with ambiguous volatility and subjective risk premium. I show that ambiguity aversion of a rational individual decreases her market participation. The aggregate premium is computed explicitly which is decomposed into three parts. Opposite signs between the rates of ambiguity premium and risk premium demonstrate that a decrease in ambiguity premium on volatility gives rise to an increase in risk premium.Kelly criterion for the wealth process to reach a goal is also studied under such ambiguous market. Ambiguity of stock appreciation rate results in investors' withdraw from markets whereas in a single-priced market, investors always trade with the market if no short-sale constraints and no transaction cost.