We model the behaviour of a stock price process under the assumption of the existence of a suppor... more We model the behaviour of a stock price process under the assumption of the existence of a support/resistance level, which is one of the most popular approaches in the field of technical analysis. We obtain optimal dynamic trading strategies under the setup.
We study the regularity of the stochastic representation of the solution of a class of initial-bo... more We study the regularity of the stochastic representation of the solution of a class of initial-boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal stopping problem such as the price of an American-style option in finance. We show continuity and smoothness of the value function using coupling and time-change techniques. As an application, we find the minimal payoff scenario for the holder of an American-style option in the presence of regime-switching uncertainty under the assumption that the transition rates are known to lie within level-dependent compact sets.
Abstract. We consider the problem of representing claims for coherent risk measures. For this pur... more Abstract. We consider the problem of representing claims for coherent risk measures. For this purpose we introduce the concept of (weak and strong) time-consistency with respect to a portfolio of assets, generalizing the one defined in Delbaen [7]. In a similar way we extend the notion of m-stability, by introducing weak and strong versions. We then prove that the two concepts of m- stability and time-consistency are still equivalent, thus giving necessary and sufficient conditions for a coherent risk measure to be represented by a market with proportional transaction costs. We go on to deduce that, under a separability assumption, any coherent risk measure is strongly time-consistent with respect to a suitably chosen countable portfolio, and show the converse: that any market with proportional transaction costs is equivalent to a market priced by a coherent risk measure, essentially establishing the equivalence of the two concepts.
We model the behaviour of a stock price process under the assumption of the existence of a suppor... more We model the behaviour of a stock price process under the assumption of the existence of a support/resistance level, which is one of the most popular approaches in the field of technical analysis. We obtain optimal dynamic trading strategies under the setup.
We study the regularity of the stochastic representation of the solution of a class of initial-bo... more We study the regularity of the stochastic representation of the solution of a class of initial-boundary value problems related to a regime-switching diffusion. This representation is related to the value function of a finite-horizon optimal stopping problem such as the price of an American-style option in finance. We show continuity and smoothness of the value function using coupling and time-change techniques. As an application, we find the minimal payoff scenario for the holder of an American-style option in the presence of regime-switching uncertainty under the assumption that the transition rates are known to lie within level-dependent compact sets.
Abstract. We consider the problem of representing claims for coherent risk measures. For this pur... more Abstract. We consider the problem of representing claims for coherent risk measures. For this purpose we introduce the concept of (weak and strong) time-consistency with respect to a portfolio of assets, generalizing the one defined in Delbaen [7]. In a similar way we extend the notion of m-stability, by introducing weak and strong versions. We then prove that the two concepts of m- stability and time-consistency are still equivalent, thus giving necessary and sufficient conditions for a coherent risk measure to be represented by a market with proportional transaction costs. We go on to deduce that, under a separability assumption, any coherent risk measure is strongly time-consistent with respect to a suitably chosen countable portfolio, and show the converse: that any market with proportional transaction costs is equivalent to a market priced by a coherent risk measure, essentially establishing the equivalence of the two concepts.
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