Cadogan, Godfrey (2009): On behavioral Arrow Pratt risk process with applications to risk pricing, stochastic cash flows, and risk control.

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Abstract
We introduce a closed form behavioural stochastic ArrowPratt risk process, decomposed into discrete asymmetric risk seeking and risk averse components that run on different local times in ϵdisks centered at risk free states. Additionally, we embed ArrowPratt (“AP”) risk measure in a simple dynamic system of discounted cash flows with constant volatility, and time varying drift. Signal extraction of ArrowPratt risk measure shows that it is highly nonlinear in constant volatility for cash flows. Robust identifying restrictions on the system solution confirm that even for small time periods constant volatility is not a measure of AP risk. By contrast, timevarying volatility measures aspects of embedded AP risk. Whereupon maximal AP risk measure is obtained from a convolution of input volatility and idiosyncratic shocks to the system. We provide four applications for our theory. First, we find that Engle, Ng and Rothschild (1990) FactorARCH model for risk premia is misspecified because the factor price of risk is time varying and unstable. Our theory predicts that a hyperARCH correction factor is required to remove the FactorARCH specification. Second, when applied to analysts beliefs about interest rates and volatility, we find that AP risk measure is a feedback control over stochastic cash flows. Whereupon increased risk aversion to negative shocks to earnings increases volatility. Third, we use an oft cited example of Benes, Shepp and Witsenhausen (1980) to characterize a controlled AP diffusion for a conservative investor who wants to minimize the AP risk process for an asset. Fourth, we recover stochastic differential utility functional from the AP risk process and show how it is functionally equivalent to Duffie and Epstein’s (1992) parametrization.
Item Type:  MPRA Paper 

Original Title:  On behavioral Arrow Pratt risk process with applications to risk pricing, stochastic cash flows, and risk control 
Language:  English 
Keywords:  behavioural ArrowPratt risk process; asymmetric risk decomposition; asset pricing; Markov process; local martingale; local time change 
Subjects:  D  Microeconomics > D0  General > D03  Behavioral Economics; Underlying Principles G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing; Trading volume; Bond Interest Rates C  Mathematical and Quantitative Methods > C0  General > C00  General G  Financial Economics > G3  Corporate Finance and Governance > G31  Capital Budgeting; Fixed Investment and Inventory Studies; Capacity 
Item ID:  20174 
Depositing User:  godfrey cadogan 
Date Deposited:  27. Jan 2010 06:58 
Last Modified:  16. Feb 2013 08:08 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/20174 