25,030 research outputs found
Valuation and hedging of the ruin-contingent life annuity (RCLA)
This paper analyzes a novel type of mortality contingent-claim called a
ruin-contingent life annuity (RCLA). This product fuses together a
path-dependent equity put option with a "personal longevity" call option. The
annuitant's (i.e. long position) payoff from a generic RCLA is \$1 of income
per year for life, akin to a defined benefit pension, but deferred until a
pre-specified financial diffusion process hits zero. We derive the PDE and
relevant boundary conditions satisfied by the RCLA value (i.e. the hedging
cost) assuming a complete market where No Arbitrage is possible. We then
describe some efficient numerical techniques and provide estimates of a typical
RCLA under a variety of realistic parameters.
The motivation for studying the RCLA on a stand-alone basis is two-fold.
First, it is implicitly embedded in approximately \$1 trillion worth of U.S.
variable annuity (VA) policies; which have recently attracted scrutiny from
financial analysts and regulators. Second, the U.S. administration - both
Treasury and Department of Labor - have been encouraging Defined Contribution
(401k) plans to offer stand-alone longevity insurance to participants, and we
believe the RCLA would be an ideal and cost effective candidate for that job
Designing A Composite Dictionary Adaptively From Joint Examples
We study the complementary behaviors of external and internal examples in
image restoration, and are motivated to formulate a composite dictionary design
framework. The composite dictionary consists of the global part learned from
external examples, and the sample-specific part learned from internal examples.
The dictionary atoms in both parts are further adaptively weighted to emphasize
their model statistics. Experiments demonstrate that the joint utilization of
external and internal examples leads to substantial improvements, with
successful applications in image denoising and super resolution
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