On Conditional Lower Partial Moments and Its Applications

SYNOPTIC ABSTRACT Lower partial moments (LPM) are predominantly used in portfolio theory and in areas involving financial risk, which addresses the problem of managing risky investment policies with the object of maximizing returns. LPM also plays an important role in the analysis of risks in income (poverty) studies. In this article, we extend the notion of LPM to the conditional set up and study its usefulness in the context of stochastic modeling. The relationship between various measures in reliability studies, income (poverty) studies, and risk analysis are also proved. Finally, a non-parametric estimator for conditional LPM is proposed and has been validated through simulated and real data sets.

[1]  Samuel Kotz,et al.  Multivariate Pareto Distributions , 2005 .

[2]  H. Levy.  Stochastic dominance and expected utility: survey and analysis , 1992 .

[3]  P. Fishburn.  Mean-Risk Analysis with Risk Associated with Below-Target Returns , 1977 .

[4]  U. V. Naik-Nimbalkar,et al.  Accelerated Failure Time Models For Load Sharing Systems , 2014, IEEE Transactions on Reliability.

[5]  V. Bawa.  OPTIMAL, RULES FOR ORDERING UNCERTAIN PROSPECTS+ , 1975 .

[6]  Vijay S. Bawa,et al.  Safety-First, Stochastic Dominance, and Optimal Portfolio Choice , 1978, Journal of Financial and Quantitative Analysis.

[7]  Dilip Roy,et al.  A CHARACTERIZATION OF MODEL APPROACH FOR GENERATING BIVARIATE LIFE DISTRIBUTIONS USING REVERSED HAZARD RATES , 2002 .

[8]  S. Sunoj,et al.  The role of lower partial moments in stochastic modeling , 2008 .

[9]  B. Arnold,et al.  Conditional specification of statistical models , 1999 .

[10]  M. Unser.  Lower partial moments as measures of perceived risk: An experimental study , 2000 .

[11]  M. Brzeziński.  Do Wealth Distributions Follow Power Laws? Evidence from 'Rich Lists' , 2013, 1304.0212.

[12]  Marco Scarsini,et al.  A note on stochastic dominance and inequality measures , 1989 .

[13]  Jane B. Adams,et al.  Major issues related to hedge accounting , 1995 .

[14]  Chanchal Kundu,et al.  Characterizations based on higher order and partial moments of inactivity time , 2017 .

[15]  William W. Hogan,et al.  Computation of the Efficient Boundary in the E-S Portfolio Selection Model , 1972, Journal of Financial and Quantitative Analysis.

[16]  B. Arnold,et al.  Bivariate Distributions with Exponential Conditionals , 1988 .

[17]  Franco Peracchi,et al.  On Estimating the Conditional Expected Shortfall , 2008 .

[18]  Amit Ghosh,et al.  Chernoff distance for conditionally specified models , 2018 .