Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userReducing the debt : is it optimal to outsource an investment?
127
0
0.0
(
0
)
Added by
Benjamin Jourdain
Publication date
2013
fields
Financial
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We deal with the problem of outsourcing the debt for a big investment, according two situations: either the firm outsources both the investment (and the associated debt) and the exploitation to a private consortium, or the firm supports the debt and the investment but outsources the exploitation. We prove the existence of Stackelberg and Nash equilibria between the firm and the private consortium, in both situations. We compare the benefits of these contracts. We conclude with a study of what happens in case of incomplete information, in the sense that the risk aversion coefficient of each partner may be unknown by the other partner.
rate research
Read More
In this paper we consider a variation of the Mertons problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under some assumptions on the underlying process and the utility function. The resulting parabolic PDE is often quite difficult to solve, even when it is linear. The present paper contributes to the pool of explicit solutions for stochastic optimal control problems. Our main result is the exact solution for optimal investment in Heston model.
We investigate an optimal investment-consumption and optimal level of insurance on durable consumption goods with a positive loading in a continuous-time economy. We assume that the economic agent invests in the financial market and in durable as well as perishable consumption goods to derive utilities from consumption over time in a jump-diffusion market. Assuming that the financial assets and durable consumption goods can be traded without transaction costs, we provide a semi-explicit solution for the optimal insurance coverage for durable goods and financial asset. With transaction costs for trading the durable good proportional to the total value of the durable good, we formulate the agents optimization problem as a combined stochastic and impulse control problem, with an implicit intervention value function. We solve this problem numerically using stopping time iteration, and analyze the numerical results using illustrative examples.
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by Levy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the Levy process with a high order scheme for the Brownian driven component, applied between the jump times. The overall approximation is analyzed using a stochastic splitting argument. The resulting error bound involves separate contributions of the compound Poisson approximation and of the discretization scheme for the Brownian part, and allows, on one hand, to balance the two contributions in order to minimize the computational time, and on the other hand, to study the optimal design of the approximating compound Poisson process. For driving processes whose Levy measure explodes near zero in a regularly varying way, this procedure allows to construct discretization schemes with arbitrary order of convergence.
Stochastic volatility models based on Gaussian processes, like fractional Brownian motion, are able to reproduce important stylized facts of financial markets such as rich autocorrelation structures, persistence and roughness of sample paths. This is made possible by virtue of the flexibility introduced in the choice of the covariance function of the Gaussian process. The price to pay is that, in general, such models are no longer Markovian nor semimartingales, which limits their practical use. We derive, in two different ways, an explicit analytic expression for the joint characteristic function of the log-price and its integrated variance in general Gaussian stochastic volatility models. Such analytic expression can be approximated by closed form matrix expressions. This opens the door to fast approximation of the joint density and pricing of derivatives on both the stock and its realized variance using Fourier inversion techniques. In the context of rough volatility modeling, our results apply to the (rough) fractional Stein--Stein model and provide the first analytic formulae for option pricing known to date, generalizing that of Stein--Stein, Sch{o}bel-Zhu and a special case of Heston.
We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued c`adl`ag functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t). We obtain some general results of convergence of this sequence. Then, we apply them to Brownian diffusions and solutions to Levy driven SDEs under some Lyapunov-type stability assumptions. As a numerical application of this work, we show that this procedure gives an efficient way of option pricing in stochastic volatility models.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
