LEARNING AND PORTFOLIO DECISIONS FOR CRRA INVESTORS

2016 ◽  
Vol 19 (03) ◽  
pp. 1650018 ◽  
Author(s):  
MICHELE LONGO ◽  
ALESSANDRA MAININI
Keyword(s):  
Market Price ◽  
Random Variable ◽  
Risk Tolerance ◽  
Partial Observation ◽  
Market Price Of Risk ◽  
Absolute Value ◽  
Portfolio Decisions ◽  
Price Of Risk ◽  
Myopic Policy ◽  
Hedging Demand

We maximize the expected utility from terminal wealth for a Constant Relative Risk Aversion (CRRA) investor when the market price of risk is an unobservable random variable and explore the effects of learning by comparing the optimal portfolio under partial observation with the corresponding myopic policy. In particular, we show that, for a market price of risk constant in sign, the ratio between the portfolio under partial observation and its myopic counterpart increases with respect to risk tolerance. As a consequence, the absolute value of the partial observation case is larger (smaller) than the myopic one if the investor is more (less) risk tolerant than the logarithmic investor. Moreover, our explicit computations enable to study in detail the so called hedging demand induced by parameter uncertainty.

scholarly journals Lévy information and the aggregation of risk aversion

2013 ◽  
Vol 469 (2154) ◽  
pp. 20130024 ◽  
Author(s):  
Dorje C. Brody ◽  
Lane P. Hughston
Keyword(s):  
General Scheme ◽  
Market Price ◽  
Random Variable ◽  
Information Process ◽  
Pricing Kernel ◽  
Market Price Of Risk ◽  
Market Pricing ◽  
Price Of Risk ◽  
Pricing Kernels ◽  
The Individual

When investors have heterogeneous attitudes towards risk, it is reasonable to assume that each investor has a pricing kernel, and that these individual pricing kernels are aggregated to form a market pricing kernel. The various investors are then buyers or sellers depending on how their individual pricing kernels compare with that of the market. In Brownian-based models, we can represent such heterogeneous attitudes by letting the market price of risk be a random variable, the distribution of which corresponds to the variability of attitude across the market. If the flow of market information is determined by the movements of prices, then neither the Brownian driver nor the market price of risk are directly visible: the filtration is generated by an ‘information process’ given by a combination of the two. We show that the market pricing kernel is then given by the harmonic mean of the individual pricing kernels associated with the various market participants. Remarkably, with an appropriate definition of Lévy information one draws the same conclusion in the case when asset prices can jump. As a consequence, we are led to a rather general scheme for the management of investments in heterogeneous markets subject to jump risk.

scholarly journals Implicit incentives for fund managers with partial information

2021 ◽  
Author(s):  
Flavio Angelini ◽  
Katia Colaneri ◽  
Stefano Herzel ◽  
Marco Nicolosi
Keyword(s):  
Asset Allocation ◽  
Partial Information ◽  
Market Price ◽  
Investment Strategy ◽  
Expected Returns ◽  
Martingale Method ◽  
Fund Manager ◽  
Market Price Of Risk ◽  
Fund Managers ◽  
Price Of Risk

AbstractWe study the optimal asset allocation problem for a fund manager whose compensation depends on the performance of her portfolio with respect to a benchmark. The objective of the manager is to maximise the expected utility of her final wealth. The manager observes the prices but not the values of the market price of risk that drives the expected returns. Estimates of the market price of risk get more precise as more observations are available. We formulate the problem as an optimization under partial information. The particular structure of the incentives makes the objective function not concave. Therefore, we solve the problem by combining the martingale method and a concavification procedure and we obtain the optimal wealth and the investment strategy. A numerical example shows the effect of learning on the optimal strategy.

Multidimensional Models: Martingale Approach

2019 ◽  
pp. 191-201
Author(s):  
Tomas Björk
Keyword(s):  
Market Price ◽  
Representation Formula ◽  
Explicit Representation ◽  
Martingale Measure ◽  
Market Price Of Risk ◽  
Martingale Approach ◽  
Price Of Risk ◽  
Equivalent Martingale ◽  
Absence Of Arbitrage ◽  
Multidimensional Models

In this chapter we study a very general multidimensional Wiener-driven model using the martingale approach. Using the Girsanov Theorem we derive the martingale equation which is used to find an equivalent martingale measure. We provide conditions for absence of arbitrage and completeness of the model, and we discuss hedging and pricing. For Markovian models we derive the relevant pricing PDE and we also provide an explicit representation formula for the stochastic discount factor. We discuss the relation between the market price of risk and the Girsanov kernel and finally we derive the Hansen–Jagannathan bounds for the Sharpe ratio.

A Primer on Incomplete Markets

2019 ◽  
pp. 128-137
Author(s):  
Tomas Björk
Keyword(s):  
Incomplete Markets ◽  
Factor Model ◽  
Market Price ◽  
Market Price Of Risk ◽  
Market Incompleteness ◽  
Price Of Risk

We discuss market incompleteness within the relatively simple framework of a factor model. The corresponding pricing PDE is derived and we relate it to the market price of risk.

scholarly journals The Market Price of Risk in Interest Rate Swaps: The Roles of Default and Liquidity Risks*

2006 ◽  
Vol 79 (5) ◽  
pp. 2337-2359 ◽  
Author(s):  
Jun Liu ◽  
Francis A. Longstaff ◽  
Ravit E. Mandell
Keyword(s):  
Interest Rate ◽  
Market Price ◽  
Market Price Of Risk ◽  
Interest Rate Swaps ◽  
Price Of Risk

scholarly journals Classifying financial markets up to isomorphism

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200264
Author(s):  
J. Armstrong
Keyword(s):  
Financial Markets ◽  
Mutual Fund ◽  
Continuous Time ◽  
Automorphism Groups ◽  
Market Price ◽  
Complete Markets ◽  
Market Price Of Risk ◽  
Isomorphism Classes ◽  
Price Of Risk ◽  
The Absolute

Two markets should be considered isomorphic if they are financially indistinguishable. We define a notion of isomorphism for financial markets in both discrete and continuous time. We then seek to identify the distinct isomorphism classes, that is to classify markets. We classify complete one-period markets. We define an invariant of continuous-time complete markets which we call the absolute market price of risk. This invariant plays a role analogous to the curvature in Riemannian geometry. We classify markets when the absolute market price of risk is deterministic. We show that, in general, markets with non-trivial automorphism groups admit mutual fund theorems. We prove a number of such theorems.

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