Nested Stochastic Modeling

Nested stochastic modeling for insurance companies

With the development of computational technology, nested stochastic modeling has become a possibility, where just a few years ago, it was an actuary’s dream. However, as the insurance industry’s regulatory requirements move more towards dependence on stochastic approaches, it has become increasingly difficult to run nested modeling. While the insurance industry continues to rely heavily on hardware innovations, trying to make brute force methods faster and more palatable, we are approaching a crossroads about how to proceed.

This work is commissioned by the Society of Actuaries in Fall 2015 to conduct an industry survey on current market practices of nested stochastic modeling and to perform a research study on computational methodologies to accelerate run time and improve model efficiency.

Research findings can be found at

Sample recycling method – a new approach to efficient nested simulations

Nested stochastic modeling has been on the rise in many fields of the financial industry. Nested stochastic models refer to stochastic models embedded inside other stochastic models. Well-known examples include portfolio risk management in the banking sector and principle-based reserving and capital requirements in the insurance sector. As the value of any financial instrument may change in response to economic conditions, the risk management of a portfolio often requires the assessment of value range of individual instruments with various risk factors in the immediate future. The valuation of individual instrument is based on projections of cashflows and risk factors into the distant future. The nesting of such stochastic modeling can be extremely computationally challenging.

Most of existing techniques to speed up nested simulation are based on curve fitting, which is to establish a functional relationship between inner loop estimator and economic scenarios and to replace inner loop simulations with the fitted curve. This paper presents a unconventional approach, which is to run inner loop estimation for a small set of outer loop scenarios and to find estimates under other outer loop scenarios by recycling inner loop paths. This new approach can be much more efficient when curve fittings are difficult to achieve in practice.

R. Feng and P. Li (2020) Sample recycling method – a new approach to efficient nested simulations. Available upon request.

Runhuan Feng
Runhuan Feng


Associate Professor

Director of Actuarial Science

H.P. Petit Professorial Scholar

State Farm Companies Foundation Scholar