We explore martingale and convex duality techniques to study optimal investment strategies that maximize expected risk-averse utility from consumption and terminal wealth in a pure-jump model driven by (multivariate) marked point processes and in presence of margin requirements such as different interest rates for borrowing and lending and risk premiums for short positions . Margin requirements are modelled by adding in a margin payment function to the investor's wealth equation which is nonlinear with respect to the portfolio proportion process . We give sufficient conditions for existence of optimal policies and find closed-form solutions for the optimal value function in the case of pure-jump models with jump-size distributions modulated by a two-state Markov chain and agents with logarithmic and fractional power utility .
We explore martingale and convex duality techniques to study optimal investment strategies that maximize expected risk-averse utility from consumption and terminal wealth . We consider a market model with jumps driven by (multivariate) marked point processes and so-called non-linear wealth dynamics which allows to take account of relaxed assumptions such as differential borrowing and lending interest rates or short positions with cash collateral and negative rebate rates . We give suffcient conditions for existence of optimal policies for agents with logarithmic and CRRA power utility. We find closed-form solutions for the optimal value function in the case of pure-jump models with jump-size distributions modulated by a two-state Markov chain .
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in a pure-jump model
. We consider a market model with jumps
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in presence of margin requirements such as different interest rates for
so-called non-linear wealth dynamics which allows to take account of relaxed assumptions such as differential
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and risk premiums for short positions . Margin requirements are modelled by adding in a margin payment function to the investor's wealth equation which is nonlinear with respect to the portfolio proportion process
interest rates or short positions with cash collateral and negative rebate rates
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sufficient
suffcient
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and
for agents with logarithmic and CRRA power utility. We
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and agents with logarithmic and fractional power utility