A stability criterion for two timescale stochastic approximation schemes

Automatica ◽  
2017 ◽  
Vol 79 ◽  
pp. 108-114 ◽  
Author(s):  
Chandrashekar Lakshminarayanan ◽  
Shalabh Bhatnagar
Keyword(s):  
Stochastic Approximation ◽  
Stability Criterion ◽  
Approximation Schemes ◽  
Two Timescale Stochastic Approximation

A two Timescale Stochastic Approximation Scheme for Simulation-Based Parametric Optimization

1998 ◽  
Vol 12 (4) ◽  
pp. 519-531 ◽  
Author(s):  
Shalabh Bhatnagar ◽  
Vivek S. Borkar
Keyword(s):  
Stochastic Approximation ◽  
Perturbation Analysis ◽  
Parametric Optimization ◽  
Approximation Scheme ◽  
Infinitesimal Perturbation Analysis ◽  
Simulation Based ◽  
Infinitesimal Perturbation ◽  
Two Timescale Stochastic Approximation

A two timescale stochastic approximation scheme which uses coupled iterations is used for simulation-based parametric optimization as an alternative to traditional “infinitesimal perturbation analysis” schemes. It avoids the aggregation of data present in many other schemes. Its convergence is analyzed, and a queueing example is presented.

scholarly journals Stochastic approximation schemes for economic capital and risk margin computations

2019 ◽  
Vol 65 ◽  
pp. 182-218 ◽  
Author(s):  
David Barrera ◽  
Stéphane Crépey ◽  
Babacar Diallo ◽  
Gersende Fort ◽  
Emmanuel Gobet ◽  
...  
Keyword(s):  
At Risk ◽  
Monte Carlo ◽  
Stochastic Approximation ◽  
Value At Risk ◽  
Expected Shortfall ◽  
Point Of View ◽  
Economic Capital ◽  
Approximation Schemes ◽  
Risk Margin ◽  
A Value

We consider the problem of the numerical computation of its economic capital by an insurance or a bank, in the form of a value-at-risk or expected shortfall of its loss over a given time horizon. This loss includes the appreciation of the mark-to-model of the liabilities of the firm, which we account for by nested Monte Carlo à la Gordy and Juneja [17] or by regression à la Broadie, Du, and Moallemi [10]. Using a stochastic approximation point of view on value-at-risk and expected shortfall, we establish the convergence of the resulting economic capital simulation schemes, under mild assumptions that only bear on the theoretical limiting problem at hand, as opposed to assumptions on the approximating problems in [17] and [10]. Our economic capital estimates can then be made conditional in a Markov framework and integrated in an outer Monte Carlo simulation to yield the risk margin of the firm, corresponding to a market value margin (MVM) in insurance or to a capital valuation adjustment (KVA) in banking parlance. This is illustrated numerically by a KVA case study implemented on GPUs.

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