  Nested stochastic modeling has been on the rise in many fields of the
financial industry. Such modeling arises whenever certain components of a
stochastic model are stochastically determined by other models. There are at
least two main areas of applications, including (1) portfolio risk management
in the banking sector and (2) principle-based reserving and capital
requirements in the insurance sector. As financial instrument values often
change with economic fundamentals, the risk management of a portfolio (outer
loop) often requires the assessment of financial positions subject to changes
in risk factors in the immediate future. The valuation of financial position
(inner loop) is based on projections of cashflows and risk factors into the
distant future. The nesting of such stochastic modeling can be computationally
challenging.
  Most of existing techniques to speed up nested simulations are based on curve
fitting. The main idea is to establish a functional relationship between inner
loop estimator and risk factors by running a limited set of economic scenarios,
and, instead of running inner loop simulations, inner loop estimations are made
by feeding other scenarios into the fitted curve. This paper presents a
non-conventional approach based on the concept of sample recycling. Its essence
is to run inner loop estimation for a small set of outer loop scenarios and to
find inner loop estimates under other outer loop scenarios by recycling those
known inner loop paths. This new approach can be much more efficient when
traditional techniques are difficult to implement in practice.
