Kernel Based Estimation of Spectral Risk Measures
Spectral risk measures (SRMs) belong to the family of coherent risk measures. A natural estimator for the class of SRMs has the form of L-statistics. Various authors have studied and derived the asymptotic properties of the empirical estimator of SRM. We propose a kernel based estimator of SRM. We investigate the large sample properties of general L-statistics based on i.i.d and dependent observations and apply them to our estimator. We prove that it is strongly consistent and asymptotically normal. We compare the finite sample performance of our proposed kernel estimator with that of several existing estimators for different SRMs using Monte Carlo simulation. We observe that our proposed kernel estimator outperforms all the estimators. Based on our simulation study we have estimated the exponential SRM of four future indices-that is Nikkei 225, Dax, FTSE 100, and Hang Seng. We also discuss the use of SRM in setting initial margin requirements of clearinghouses. Finally we perform a backtesting exercise of SRM.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning
We propose a novel framework to solve risk-sensitive reinforcement learning (RL) problems where the agent optimises time-consistent dynamic spectral risk measures. Based on the notion of conditional elicitability, our me…
Deep Reinforcement Learningreinforcement-learningReinforcement LearningReinforcement Learning (RL)Non-asymptotic estimation of risk measures using stochastic gradient Langevin dynamics
In this paper we will study the approximation of arbitrary law invariant risk measures. As a starting point, we approximate the average value at risk using stochastic gradient Langevin dynamics, which can be seen as a va…
Risk Estimation in a Markov Cost Process: Lower and Upper Bounds
We tackle the problem of estimating risk measures of the infinite-horizon discounted cost within a Markov cost process. The risk measures we study include variance, Value-at-Risk (VaR), and Conditional Value-at-Risk (CVa…
Estimation of Spectral Risk Measures
We consider the problem of estimating a spectral risk measure (SRM) from i.i.d. samples, and propose a novel method that is based on numerical integration. We show that our SRM estimate concentrates exponentially, when t…
Numerical IntegrationA Wasserstein distance approach for concentration of empirical risk estimates
This paper presents a unified approach based on Wasserstein distance to derive concentration bounds for empirical estimates for two broad classes of risk measures defined in the paper. The classes of risk measures introd…