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Risk lovers, mixed risk loving and the preference to combine good with good

This paper examines the concept of 'risk loving' (that is risk seeking, intemperance, edginess, etc.), which can be characterised by preferences over simple lotteries. This paper analyses the notion of preferring to combine good with good, and bad with bad, as opposed to combining good with bad as usual. The significance of such preferences has implications on utility functions and are analysed in the paper. This paper extends Eeckhoudt and Schlesinger (2006) results to risk lovers, the results from Crainich et al. (2013) are also generalised to higher orders. We also generalise to higher orders the concept of bivariate risk seeking, introduced by Richard (1975) and called correlation loving by Epstein and Tanny (1980). In the expected utility framework, risk loving of order (N, M) coincides with the non-negativity of the (N, M)th partial derivative of the utility function. In dealing with mixed risk loving utility functions, we give several useful properties, for example, mixed risk loving is consistent with the mixture of positive exponential utilities and with non-increasing coefficients of absolute risk aversion at any order.