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 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.

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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