Conditioning super-Brownian motion on its boundary statistics, and fragmentation

We condition super-Brownian motion on "boundary statistics" of the exit measure $X_D$ from a bounded domain $D$. These are random variables defined on an auxiliary probability space generated by sampling from the exit measure $X_D$. Two particular examples are: conditioning on a Poisson random measure with intensity $\beta X_D$ and conditioning on $X_D$ itself. We find the conditional laws as $h$-transforms of the original SBM law using Dynkin's formulation of $X$-harmonic functions. We give explicit expression for the (extended) $X$-harmonic functions considered. We also obtain explicit constructions of these conditional laws in terms of branching particle systems. For example, we give a fragmentation system description of the law of SBM conditioned on $X_D=\nu$, in terms of a particle system, called the backbone. Each particle in the backbone is labeled by a measure $\tilde{\nu}$, representing its descendants' total contribution to the exit measure. The particle's spatial motion is an $h$-transform of Brownian motion, where $h$ depends on $\tilde{\nu}$. At the particle's death two new particles are born, and $\tilde{\nu}$ is passed to the newborns by fragmentation.Comment: Published in at http://dx.doi.org/10.1214/12-AOP778 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

Computed tomography measures of nutrition in patients with end-stage liver disease provide a novel approach to characterize deficits

Aim Patients with cirrhosis and end-stage liver disease (ESLD) develop severe nutrition deficits that impact on morbidity and mortality. Laboratory measures of nutrition fail to fully assess clinical deficits in muscle mass and fat stores. This study employs computed tomography imaging to assess muscle mass and subcutaneous and visceral fat stores in patients with ESLD. Methods This 1:1 case-control study design compares ESLD patients with healthy controls. Study patients were selected from a database of ESLD patients using a stratified method to assure a representative sample based on age, body mass index (BMI), gender, and model for end-stage liver disease score (MELD). Control patients were trauma patients with a low injury severity score (<10) who had a CT scan during evaluation. Cases and controls were matched for age +/- 5 years, gender, and BMI +/- 2. Results There were 90 subjects and 90 controls. ESLD patients had lower albumin levels (p<0.001), but similar total protein levels (p=0.72). ESLD patients had a deficit in muscle mass (-19%, p<0.001) and visceral fat (-13%, p<0.001), but similar subcutaneous fat (-1%, p=0.35). ESLD patients at highest risk for sarcopenia included those over age 60, BMI< 25.0, and female gender. We found degree of sarcopenia to be independent of MELD score. Conclusions These results support previous research demonstrating substantial nutrition deficits in ESLD patients that are not adequately measured by laboratory testing. Patients with ESLD have significant deficits of muscle and visceral fat stores, but a similar amount of subcutaneous fat

Optimal initiation of a GLWB in a variable annuity: no arbitrage approach

This paper offers a financial economic perspective on the optimal time (and age) at which the owner of a Variable Annuity (VA) policy with a Guaranteed Living Withdrawal Benefit (GLWB) rider should initiate guaranteed lifetime income payments. We abstract from utility, bequest and consumption preference issues by treating the VA as liquid and tradable. This allows us to use an American option pricing framework to derive a so-called optimal initiation region. Our main practical finding is that given current design parameters in which volatility (asset allocation) is restricted to less than 20%, while guaranteed payout rates (GPR) as well as bonus (roll-up) rates are less than 5%, GLWBs that are in-the-money should be turned on by the late 50s and certainly the early 60s. The exception to the rule is when a non-constant GPR is about to increase (soon) to a higher age band, in which case the optimal policy is to wait until the new GPR is hit and then initiate immediately. Also, to offer a different perspective, we invert the model and solve for the bonus (roll-up) rate that is required to justify delaying initiation at any age. We find that the required bonus is quite high and more than what is currently promised by existing products. Our methodology and results should be of interest to researchers as well as to the individuals that collectively have over \$1 USD trillion in aggregate invested in these products. We conclude by suggesting that much of the non-initiation at older age is irrational (which obviously benefits the insurance industry.