If Bitcoin becomes the prevalent payment system on the Internet, crime fighters will join forces with regulators and enforce blacklisting of transaction prefixes at the parties who offer real products and services in exchange for bitcoin. Blacklisted bitcoins will be hard to spend and therefore less liquid and less valuable. This requires every recipient of Bitcoin payments not only to check al...

Merton Model is one of the famous credit risk models. This model presumes that the only source of uncertainty in equity prices is the firm’s net asset value .But the above market condition holds only when the market is efficient which is often been ignored in modern research. Another, the original Merton Model is based on assumptions that in the event of default absolute priority holds, renegot...

1 This is the written version of the Cattedra Galileana lectures, Scuola Normale Supe-riore, in Pisa, 2002, made possible through the wonderful organizational work of Maurizio Pratelli, to whom I am most grateful. I am also grateful for support for the course offered by the Associazione Amici della Scuola Normale Superiore, who were generously represented by Mr. Carlo Gulminelli.

This paper estimates a consumption-based, no-arbitrage model of the term structure of real interest rates. The model nests the standard long-run risk model which assumes constant market prices of risk. We find that the long-run consumption risk dominates the short-run and volatility risks and drives most of the movements of bond risk premiums. The risk premium for consumption volatility is nega...

This paper is concerned with the stochastic comparison of two individual risk models for homogeneous portfolios with different claim size distributions. It is shown that a Lorenz order between the claim sizes, or a hamr-order if the claim sizes are NBUE, are transferred to the corresponding individual risk models. © 2001 Elsevier Science B.V. All rights reserved.

We discuss when and why custom multi-factor risk models are warranted and give source code for computing some risk factors. Pension/mutual funds do not require customization but standardization. However, using standardized risk models in quant trading with much shorter holding horizons is suboptimal: (1) longer horizon risk factors (value, growth, etc.) increase noise trades and trading costs; ...

In this paper, we consider some non-standard renewal risk models with some dependent claim sizes and stochastic return, where an insurance company is allowed to invest her/his wealth in financial assets, and the price process of the investment portfolio is described as a geometric Lévy process. When the claim-size distribution belongs to some classes of heavy-tailed distributions and a constrai...

We consider the Erlang(λ, n) risk process with i.i.d. exponentially distributed claims severities. We prove that the ruin probability is a strictly decreasing function in n if we keep the expected interarrival times between two successive claims constant. In the limit case we obtain Lundberg’s fundamental equation in the discrete time risk model (ladder heights of random walks).