All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 13 of 13

Showing per page

Real-valued conditional convex risk measures in Lp(ℱ, R)

Treviño-Aguilar Erick (2011)

ESAIM: Proceedings

The numerical representation of convex risk measures beyond essentially bounded financial positions is an important topic which has been the theme of recent literature. In other direction, it has been discussed the assessment of essentially bounded risks taking explicitly new information into account, i.e., conditional convex risk measures. In this paper we combine these two lines of research. We discuss the numerical representation of conditional...

Refined wing asymptotics for the Merton and Kou jump diffusion models

Stefan Gerhold, Johannes F. Morgenbesser, Axel Zrunek (2015)

Banach Center Publications

Refining previously known estimates, we give large-strike asymptotics for the implied volatility of Merton's and Kou's jump diffusion models. They are deduced from call price approximations by transfer results of Gao and Lee. For the Merton model, we also analyse the density of the underlying and show that it features an interesting "almost power law" tail.

Representation of Itô integrals by Lebesgue/Bochner integrals

Qi Lü, Jiongmin Yong, Xu Zhang (2012)

Journal of the European Mathematical Society

In [Yong 2004], it was proved that as long as the integrand has certain properties, the corresponding Itô integral can be written as a (parameterized) Lebesgue integral (or a Bochner integral). In this paper, we show that such a question can be answered in a more positive and refined way. To do this, we need to characterize the dual of the Banach space of some vector-valued stochastic processes having different integrability with respect to the time variable and the probability measure. The later...

Robust estimates of certain large deviation probabilities for controlled semi-martingales

Hideo Nagai (2015)

Banach Center Publications

Motivated by downside risk minimization on the wealth process in an incomplete market model, we have studied in the recent work the asymptotic behavior as time horizon T → ∞ of the minimizing probability that the empirical mean of a controlled semi-martingale falls below a certain level on the time horizon T. This asymptotic behavior relates to a risk-sensitive stochastic control problem in the risk-averse case. Indeed, we obtained an expression of the decay rate of the probability by the Legendre...

Robust portfolio selection under exponential preferences

Dariusz Zawisza (2010)

Applicationes Mathematicae

We consider an incomplete market with an untradable stochastic factor and a robust investment problem based on the CARA utility. We formulate it as a stochastic differential game problem, and use Hamilton-Jacobi-Bellman-Isaacs equations to derive an explicit representation of the robust optimal portfolio; the HJBI equation is transformed using a substitution of the Cole-Hopf type. Not only the pure investment problem, but also a problem of robust hedging is taken into account: an agent tries to...

Robust recursive estimation of GARCH models

Tomáš Cipra, Radek Hendrych (2018)

Kybernetika

The robust recursive algorithm for the parameter estimation and the volatility prediction in GARCH models is suggested. It seems to be useful for various financial time series, in particular for (high-frequency) log returns contaminated by additive outliers. The proposed procedure can be effective in the risk control and regulation when the prediction of volatility is the main concern since it is capable to distinguish and correct outlaid bursts of volatility. This conclusion is demonstrated by...

Robustness regions for measures of risk aggregation

Silvana M. Pesenti, Pietro Millossovich, Andreas Tsanakas (2016)

Dependence Modeling

One of risk measures’ key purposes is to consistently rank and distinguish between different risk profiles. From a practical perspective, a risk measure should also be robust, that is, insensitive to small perturbations in input assumptions. It is known in the literature [14, 39], that strong assumptions on the risk measure’s ability to distinguish between risks may lead to a lack of robustness. We address the trade-off between robustness and consistent risk ranking by specifying the regions in...

Currently displaying 1 – 13 of 13

Page 1