A convertible bond (CB) is a financial derivative, a so called hybrid security. It is an issued contract from a company or a government, which is paid for up-front. The contract yields a known amount at the specified maturity date, unless the holder chooses to convert it into an amount of the underlying asset. This kind of financial products can have complex features affecting the contract price and the optimal exercising situation. The partial differential equation (PDE) approach used for pricing financial derivatives makes it possible to describe convertible bonds with a physical model, a reversed diffusion described by a parabolic PDE. One can sometimes find both analytical and numerical solutions for this type of PDEs and interpret the solutions from a financial point of view, as they suggest predictable behaviour of the contract price.

<p>Synthesis of terrains with complex features has been a challenging problem in computer graphics since most of the existing methods are based on the height field representation. Complex features in terrains adds to the overall realism of the terrain. Hence, there is a need to synthesize terrains in real-time with complex features that adhere to user input. The methodology described in this thesis describes a novel way to synthesize terrains with complex features based on user drawn sketches. Layered stack data structure is used to ensure that the resulting terrain has complex features. Since, Neural Networks are used to generate the terrains, the process is real-time.</p>