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"Nonlinearity is an important consideration in many problems of finance and economics, such as pricing securities, computing equilibrium, and conducting structural estimations. We extend the transform analysis in Duffie, Pan, and Singleton (2000) by providing analytical treatment of a general class of nonlinear transforms for processes with tractable conditional characteristic functions. We illustrate the applications of the generalized transform method in pricing contingent claims and solving general equilibrium models with preference shocks, heterogeneous agents, or multiple goods. We also apply the method to a model of time-varying labor income risk and study the implications of stochastic covariance between labor income and dividends for the dynamics of the risk premiums on financial wealth and human capital"--National Bureau of Economic Research web site

Abstract
We consider stochastic partial differential equations appearing as Markovian lifts of matrix-valued (affine) Volterra-type processes from the point of view of the generalized Feller property (see, e.g., Dörsek and Teichmann in A semigroup point of view on splitting schemes for stochastic (partial) differential equations, 2010. arXiv:1011.2651). We introduce in particular Volterra Wishart processes with fractional kernels and values in the cone of positive semidefinite matrices. They are constructed from matrix products of infinite dimensional Ornstein–Uhlenbeck processes whose state space is the set of matrix-valued measures. Parallel to that we also consider positive definite Volterra pure jump processes, giving rise to multivariate Hawkes-type processes. We apply these affine covariance processes for multivariate (rough) volatility modeling and introduce a (rough) multivariate Volterra Heston-type model.

The development of computer technology nowadays has progressed very rapidly in line with the development of computer and telecommunication technology, making communication more open and information exchange faster, however not all developments in communication technology have had a positive and beneficial impact. One of the negative impacts of technological development is the existence of wiretapping, with the presence of encrypted tapping, the security aspect in exchanging important information. The problem of sending messages (e-mail), be its agencies, education, government, private and others, must contain confidential information, so encryption of the message is required. Encryption of information is important to support information security, because it can guarantee message security. Therefore, encryption is needed by users who have information that is guaranteed its confidentiality. One way to store data sent via email is to use cryptography. The Affine Cipher is an extension of the Caesar Cipher which multiplies the plaintext by a value and adds a shift. Creating an application by implementing cryptography using the Affine Cipher is one way of maintaining the confidentiality of information and is very important. The results obtained from this research are that the application created can change the content of existing messages and can store information that is available when sending e-mails. The process of encoding messages using the Affine Cipher algorithm is successfully used to hide secret messages into text. Keywords: Implementation, algorithm, affine cipher, data