We study the problem of asset and liability management of participating insurance policies with guarantees. We develop a scenario optimization model for integrative asset and liability management, analyze the tradeoffs in structuring such policies, and study alternative choices in funding them. The nonlinearly constrained optimization model can be linearized through closed form solutions of the...

We study how to solve sum of squares (SOS) and Lasserre’s relaxations for large scale polynomial optimization. When interior-point type methods are used, typically only small or moderately large problems could be solved. This paper proposes the regularization type methods which would solve significantly larger problems. We first describe these methods for general conic semidefinite optimization...

We study how to solve semidefinite programming (SDP) relaxations for large scale polynomial optimization. When interior-point methods are used, typically only small or moderately large problems could be solved. This paper studies regularization methods for solving polynomial optimization problems. We describe these methods for semidefinite optimization with block structures, and then apply them...