Many authors have argued, for good reasons, that in a range of applications the lens put-put law is too strong. On the other hand, the present authors have shown that very well behaved lenses, which do satisfy the put-put law by definition, are algebras for a certain monad, and that this viewpoint admits fruitful generalisations of the lens concept to a variety of base categories. In the algebr...

Option theory which has dominated residential mortgage prepayment and default research implies that a borrower will exercise prepayment or default options if the call option or put option, respectively, is "in the money" by some optimal amount. Empirical research provides evidence that the financial value of the call option is strongly associated with exercise of the prepayment option, and the ...

Most US-based insurance companies offer holders of their tax-sheltered savings plans (VAs), the long-term option to annuitise their policy at a pre-determined rate over a pre-specified period of time. Currently, there is approximately one trillion dollars invested in such policies, with guaranteed annuitisation rates, in addition to any guaranteed minimum death benefit. The insurance company ha...

One of the most widely studied problems in financial mathematics is the pricing of derivative securities, also known as contingent claims. These are securities whose price depend on the value of another underlying security. Financial options are the most common examples of derivative securities. For example, a European call option on a particular underlying security gives the holder the right t...

When categorizing water management alternatives, to meet water needs, water transfer is seen as an option that tends to supply more water. Most developing countries where limited water resources are available with high spatiotemporal dispersion, favor this option. The numbers of such projects that have been proposed, implemented, and operated in recent years evidence the desirability of this al...

The paper further develops, both from the theoretical and numerical points of view the analytic valuation of the American options, initiated by Geske and Johnson (1984) for the American put with no dividend. We present and prove closed form formulas for the Bermudan put and call, with dividend, paid continuously at a constant rate, where a general number and not necessarily equal length interva...

In this paper we show that the optimal exercise boundary/ free boundary of the American put option pricing problem for jump diffusions is continuously differentiable (except at the maturity). We also discuss the higher order regularity of the free boundary.