9,424 research outputs found
Robust maximization of asymptotic growth
This paper addresses the question of how to invest in a robust growth-optimal
way in a market where the instantaneous expected return of the underlying
process is unknown. The optimal investment strategy is identified using a
generalized version of the principal eigenfunction for an elliptic second-order
differential operator, which depends on the covariance structure of the
underlying process used for investing. The robust growth-optimal strategy can
also be seen as a limit, as the terminal date goes to infinity, of optimal
arbitrages in the terminology of Fernholz and Karatzas [Ann. Appl. Probab. 20
(2010) 1179-1204].Comment: Published in at http://dx.doi.org/10.1214/11-AAP802 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Mortgage Contracts and Underwater Default
We analyze recently proposed mortgage contracts that aim to eliminate
selective borrower default when the loan balance exceeds the house price (the
``underwater'' effect). We show contracts that automatically reduce the
outstanding balance in the event of house price decline remove the default
incentive, but may induce prepayment in low price states. However, low state
prepayments vanish if the benefit from home ownership is sufficiently high. We
also show that capital gain sharing features, such as prepayment penalties in
high house price states, are ineffective as they virtually eliminate
prepayment. For observed foreclosure costs, we find that contracts with
automatic balance adjustments become preferable to the traditional fixed-rate
contracts at mortgage rate spreads between 50-100 basis points. We obtain these
results for perpetual versions of the contracts using American options pricing
methodology, in a continuous-time model with diffusive home prices. The
contracts' values and optimal decision rules are associated with free boundary
problems, which admit semi-explicit solutions
Continuous-time perpetuities and time reversal of diffusions
We consider the problem of estimating the joint distribution of a
continuous-time perpetuity and the underlying factors which govern the cash
flow rate, in an ergodic Markov model. Two approaches are used to obtain the
distribution. The first identifies a partial differential equation for the
conditional cumulative distribution function of the perpetuity given the
initial factor value, which under certain conditions ensures the existence of a
density for the perpetuity. The second (and more general) approach, identifies
the joint law as the stationary distribution of an ergodic multi-dimensional
diffusion using techniques of time reversal. This later approach allows for
efficient use of Monte-Carlo simulation when estimating the distribution, as
the distribution is obtained by sampling a single path of the reversed process.Comment: 42 pages; added numerical exampl
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