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In this article, we extend the framework of monetary risk measures for stochastic processes to account for heavy tailed distributions of random cash flows evolving over a fixed trading horizon. To this end, we transfer the L p -duality underlying the representation of monetary risk measures to a more flexible Orlicz duality, in spaces of stochastic processes modelling random future evolution of financial values in continuous time over a finite horizon. This contributes, on the one hand, to the theory of real-valued monetary risk measures for processes and, on the other hand, supports a new representation of acceptability indices of financial performance. [ABSTRACT FROM AUTHOR]

Assume that the random future evolution of values is modelled in continuous time. Then, a risk measure can be viewed as a functional on a space of continuous-time stochastic processes. In this paper we study coherent and convex monetary risk measures on the space of all càdlàg processes that are adapted to a given filtration. We show that if such risk measures are required to be real-valued, then they can only depend on a stochastic process in a way that is uninteresting for many applications. Therefore, we allow them to take values in ( −∞, ∞]. The economic interpretation of a value of ∞ is that the corresponding financial position is so risky that no additional amount of money can make it acceptable. The main result of the paper gives different characterizations of coherent or convex monetary risk measures on the space of all bounded adapted càdlàg processes that can be extended to coherent or convex monetary risk measures on the space of all adapted càdlàg processes. As examples we discuss a new approach to measure the risk of an insurance company and a coherent risk measure for unbounded càdlàg processes induced by a so called m-stable set. [ABSTRACT FROM AUTHOR]

Assume that the random future evolution of values is modelled in continuous time. Then, a risk measure can be viewed as a functional on a space of continuous-time stochastic processes. In this paper we study coherent and convex monetary risk measures on the space of all cádlág processes that are adapted to a given filtration. We show that if such risk measures are required to be real-valued, then they can only depend on a stochastic process in a way that is uninteresting for many applications. Therefore, we allow them to take values in. The economic interpretation of a value ofis that the corresponding financial position is so risky that no additional amount of money can make it acceptable. The main result of the paper gives different characterizations of coherent or convex monetary risk measures on the space of all bounded adapted cádlág processes that can be extended to coherent or convex monetary risk measures on the space of all adapted cádlág processes. As examples we discuss a new approach to measure the risk of an insurance company and a coherent risk measure for unbounded cádlág processes induced by a so called m-stable set. [ABSTRACT FROM AUTHOR]

If the random future evolution of values is modelled in continuous time, then a risk measure can be viewed as a functional on a space of continuous-time stochastic processes. We extend the notions of coherent and convex monetary risk measures to the space of bounded càdlàg processes that are adapted to a given filtration. Then, we prove representation results that generalize earlier results for one- and multi-period risk measures, and we discuss some examples. [Copyright &y& Elsevier]