2,473 research outputs found
Maximising Survival, Growth, and Goal Reaching Under Borrowing Constraints
In this paper, we consider three problems related to survival, growth, and
goal reaching maximization of an investment portfolio with proportional net
cash flow. We solve the problems in a market constrained due to borrowing
prohibition. To solve the problems, we first construct an auxiliary market and
then apply the dynamic programming approach. Via our solutions, an alternative
approach is introduced in order to solve the problems defined under an
auxiliary market
Credit dynamics in a first passage time model with jumps
The payoff of many credit derivatives depends on the level of credit spreads. In particular, the payoff of credit derivatives with a leverage component is sensitive to jumps in the underlying credit spreads. In the framework of first passage time models we extend the model introduced in [Overbeck and Schmidt, 2005] to address these issues. In the extended a model, a credit quality process is driven by an Itô integral with respect to a Brownian motion with stochastic volatility. Using a representation of the credit quality process as a time-changed Brownian motion, we derive formulas for conditional default probabilities and credit spreads. An example for a volatility process is the square root of a Lévy-driven Ornstein-Uhlenbeck process. We show that jumps in the volatility translate into jumps in credit spreads. We examine the dynamics of the OS-model and the extended model and provide examples. --gap risk,credit spreads,credit dynamics,first passage time models,Lévy processes,general Ornstein-Uhlenbeck processes
Modeling Financial System with Interbank Flows, Borrowing, and Investing
In our model, private actors with interbank cash flows similar to, but nore
general than (Carmona, Fouque, Sun, 2013) borrow from the outside economy at a
certain interest rate, controlled by the central bank, and invest in risky
assets. Each private actor aims to maximize its expected terminal logarithmic
utility. The central bank, in turn, aims to control the overall economy by
means of an exponential utility function. We solve all stochastic optimal
control problems explicitly. We are able to recreate occasions such as
liquidity trap. We study distribution of the number of defaults (net worth of a
private actor going below a certain threshold).Comment: 27 pages, 29 figures. Keywords: systemic risk, stochastic control,
principal-agent problem, stationary distribution, stochastic stability,
Lyapunov functio
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