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We propose a general family of piecewise hyperbolic absolute risk aversion (PHARA) utility, including many non-standard utilities as examples. A typical application is the composition of an HARA preference and a piecewise linear payoff in hedge fund management. We derive a unified closed-form formula of the optimal portfolio, which is a four-term division. The formula has clear economic meanings, reflecting the behavior of risk aversion, risk seeking, loss aversion and first-order risk aversion. One main finding is that risk-taking behaviors are greatly increased by non-concavity and reduced by non-differentiability.
The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal strategies in the r
We study an optimal dividend problem for an insurer who simultaneously controls investment weights in a financial market, liability ratio in the insurance business, and dividend payout rate. The insurer seeks an optimal strategy to maximize her expec
This paper addresses the joint calibration problem of SPX options and VIX options or futures. We show that the problem can be formulated as a semimartingale optimal transport problem under a finite number of discrete constraints, in the spirit of [ar
Online portfolio selection research has so far focused mainly on minimizing regret defined in terms of wealth growth. Practical financial decision making, however, is deeply concerned with both wealth and risk. We consider online learning of portfoli
We study the problem of active portfolio management where an investor aims to outperform a benchmark strategys risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal wealth lie with