SKU: 17520006003

Generalized Integral Transforms in Mathematical Finance

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Generalized Integral Transforms in Mathematical FinanceThis book describes several techniques, first invented in physics for solving problems of heat and mass transfer, and applies them to various problems of mathematical finance defined in domains with moving boundaries. These problems include: (a) semi closed form pricing of options in the one factor models with time dependent barriers (Bachelier, Hull White, CIR, CEV); (b) analyzing an interconnected banking system in the structural credit risk model

This book describes several techniques, first invented in physics for solving problems of heat and mass transfer, and applies them to various problems of mathematical finance defined in domains with moving boundaries. These problems include: (a) semi-closed form pricing of options in the one-factor models with time-dependent barriers (Bachelier, Hull-White, CIR, CEV); (b) analyzing an interconnected banking system in the structural credit risk model with default contagion; (c) finding first hitting time density for a reducible diffusion process; (d) describing the exercise boundary of American options; (e) calculating default boundary for the structured default problem; (f) deriving a semi-closed form solution for optimal mean-reverting trading strategies; to mention but some.

 

The main methods used in this book are generalized integral transforms and heat potentials. To find a semi-closed form solution, we need to solve a linear or nonlinear Volterra equation of the second kind and then represent the option price as a one-dimensional integral. Our analysis shows that these methods are computationally more efficient than the corresponding finite-difference methods for the backward or forward Kolmogorov PDEs (partial differential equations) while providing better accuracy and stability.

 

We extend a large number of known results by either providing solutions on complementary or extended domains where the solution is not known yet or modifying these techniques and applying them to new types of equations, such as the Bessel process. The book contains several novel results broadly applicable in physics, mathematics, and engineering.

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SKU: 17520006003

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KraussRBF
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OK for Fetch, but...
Bounces well but very hard for dog to chew.
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100 PLUS STARS!!! We have a very VERY active pup (6 yrs old 🤦‍♀️🤦‍♀️)… he has destroyed EVERYTHING we have ever given him. So I ordered this AND the replacement shell. He has chewed the ball extensively but it is in PERFECT shape, no need for the replacement one YET.. I can not rave about this enough - he LOVES it, we love watching him with it and he won’t let it out of his site at all!! If we touch it he gets upset.. so when we charge it, we put the shell back together and give him that.. which reminds me - make sure you have that screwed TIGHT.. somehow he was able to get it apart.. but once we started tightening it he hasn’t been able to.. thinking about it?? GET IT!! You won’t be disappointed and neither will your dog!!
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An expensive ball to think about
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Went with the foam ball because I have hopes that my dogs teeth will sink in enough to be satisfying without having to shred it like a tennis ball. So far, so good. I chose this one because the of the outer shell replacement possibility; assurance that 30 dollars towards a ball would have an extended life option for half the price if needed. It is slightly bigger than a tennis ball and big enough for my dog to be unable to get a strong clench and crush it. He does try though and it's holding up. All of the options and modes are great. However, I wish it acted more of a bait ball. Going through all three of the modes, I can't say any have sparked a wild chase. It will bounce intermittently or once touched. The intervals are long enough to lose my dogs interests. Short intervals make the ball the easy loser every time. Better on hardwood but pathetic on carpet. It will roll but not far or very fast. The only positives from this may be the battery conservation but when he stops playing with it, it is still rolling around the room. I think it takes 20-30 minutes of inactivity for sleep mode. With this, the charge will last about a day of play. It does charge quickly. It has passed the tough chewer test with one who can chew through "tuff" toys in no time but I wish it was more of a challenge. After telling my sister i purchased one, she said she would've given me hers because her dog had lost interest. Go with your hunch and find another game to invest in if you have trepidations of this being this case. I won't deduct anymore stars because the product is as advertised. Only one deducted for the price.
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So far so good
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For the past 2 years I’ve been looking for an interactive ball our dog won’t break within days. I appreciate that it’s all foam, without any ropes or plastic pieces he can chomp on. I don’t let him use it as a chew toy but after catching it he does like to chew on it for a little bit, and it’s held up nicely after a month. Would recommend
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