SSRN Author: Ryan Francis DonnellyRyan Francis Donnelly SSRN Content
https://www.ssrn.com/author=1773967
https://www.ssrn.com/rss/en-usSun, 24 Feb 2019 01:08:12 GMTeditor@ssrn.com (Editor)Sun, 24 Feb 2019 01:08:12 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Effort Expenditure for Cash Flow in a Mean-Field EquilibriumWe study a mean-field game framework in which agents expend costly efforts in order to transition into a state where they receive cash flows. As more agents transition into the cash flow receiving state, the magnitude of all remaining cash flows decreases, introducing an element of competition whereby agents are rewarded for transitioning earlier. An equilibrium is reached if the optimal expenditure of effort produces a transition intensity which is equal to the flow rate at which the continuous population enters the receiving state. We give closed-form expressions which yield equilibrium when the cash flow horizon is infinite or exponentially distributed. When the cash flow horizon is finite we implement an algorithm which yields equilibrium if it converges. We show that in some cases a higher cost of effort results in the agents placing greater value on the potential cash flows in equilibrium. We also present cases where algorithm fails to converge to an equilibrium.
https://www.ssrn.com/abstract=3235553
https://www.ssrn.com/1765907.htmlFri, 22 Feb 2019 23:07:22 GMTREVISION: Effort Expenditure for Cash Flow in a Mean-Field EquilibriumWe study a mean-field game framework in which agents expend costly efforts in order to transition into a state where they receive cash flows. As more agents transition into the cash flow receiving state, the magnitude of all remaining cash flows decreases, introducing an element of competition whereby agents are rewarded for transitioning earlier. An equilibrium is reached if the optimal expenditure of effort produces a transition intensity which is equal to the flow rate at which the continuous population enters the receiving state. We give closed-form expressions which yield equilibrium when the cash flow horizon is infinite or exponentially distributed. When the cash flow horizon is finite we implement an algorithm which yields equilibrium if it converges. We show that in some cases a higher cost of effort results in the agents placing greater value on the potential cash flows in equilibrium. We also present cases where algorithm fails to converge to an equilibrium.
https://www.ssrn.com/abstract=3235553
https://www.ssrn.com/1720060.htmlWed, 29 Aug 2018 15:34:38 GMTREVISION: Hedging Non-Tradable Risks with Transaction Costs and Price ImpactA risk-averse agent hedges her exposure to a non-tradable risk factor U using a correlated traded asset S and accounts for the impact of her trades on both factors. The effect of the agent's trades on U is referred to as cross-impact. By solving the agent's stochastic control problem, we obtain a closed-form expression for the optimal strategy when the agent holds a linear position in U. When the exposure to the non-tradable risk factor is non-linear, we provide an approximation to the optimal strategy in closed-form, and prove that the value function is correctly approximated by this strategy when cross-impact and risk-aversion are small. We further prove that when exposure to U is non-linear, the approximate optimal strategy can be written in terms of the optimal strategy for a linear exposure with the size of the position changing dynamically according to the exposure's "Delta" under a particular probability measure.
https://www.ssrn.com/abstract=3158727
https://www.ssrn.com/1700220.htmlSat, 16 Jun 2018 09:08:51 GMTREVISION: Hedging Non-Tradable Risks with Transaction Costs and Price ImpactA risk-averse agent hedges her exposure to a non-tradable risk factor U using a correlated traded asset S and accounts for the impact of her trades on both factors. The effect of the agent's trades on U is referred to as cross-impact. By solving the agent's stochastic control problem, we obtain a closed-form expression for the optimal strategy when the agent holds a linear position in U. When the exposure to the non-tradable risk factor is non-linear, we provide an approximation to the optimal strategy in closed-form, and prove that the value function is correctly approximated by this strategy when cross-impact and risk-aversion are small. We further prove that when exposure to U is non-linear, the approximate optimal strategy can be written in terms of the optimal strategy for a linear exposure with the size of the position changing dynamically according to the exposure's "Delta" under a particular probability measure.
https://www.ssrn.com/abstract=3158727
https://www.ssrn.com/1697995.htmlWed, 06 Jun 2018 18:20:00 GMTREVISION: Substitute Hedging with Cross Price ImpactWe consider an optimal execution problem in which a risk-averse agent has exposure to a non-traded risk factor, but can trade in an asset which is correlated with the non-traded factor. The impact of the agent's trades are incorporated in the dynamics of the traded asset (price impact) and in the dynamics of the non-traded factor, which we refer to as cross impact. We solve for the optimal strategy in closed-form when the agent holds shares of a non-traded asset (linear exposure). When the exposure to the non-traded risk factor is non-linear the optimal dynamic trading strategy is approximated by a closed-form expression which applies when cross price impact and risk-aversion are small.
https://www.ssrn.com/abstract=3158727
https://www.ssrn.com/1686898.htmlFri, 27 Apr 2018 05:04:40 GMT