@Ajax.BeginForm(...., new AjaxOptions { OnSuccess = "loadDetails" })
{
...
}

<script>
     function loadDetails() { $('#linkToDetails').click(); }
</script>

 public HttpResponseMessage PutProduct(int id, Product product)
        {
            if (!ModelState.IsValid)
            {
                return Request.CreateErrorResponse(HttpStatusCode.BadRequest, ModelState);
            }

            if (id != product.Id)
            {
                return Request.CreateResponse(HttpStatusCode.BadRequest);
            }

            db.Entry(product).State = EntityState.Modified;

            try
            {
                db.SaveChanges();
            }
            catch (DbUpdateConcurrencyException ex)
            {
                return Request.CreateErrorResponse(HttpStatusCode.NotFound, ex);
            }

            return Request.CreateResponse(HttpStatusCode.OK);
        }

            <div class="editor-label">
                <label for="Name">Наименование</label>
            </div>
            <div class="editor-field">
                <input class="text-box single-line" data-val="true" data-val-required="Требуется поле Наименование ." id="Name" name="Name" type="text" value="" />
                <span class="field-validation-valid" data-valmsg-for="Name" data-valmsg-replace="true"></span>
            </div>

            <div class="editor-label">
                <label for="Name">Наименование риска</label>
            </div>
            <div class="editor-field">
                <input name="Name" class="text-box single-line input-validation-error" id="Name" type="text" value="" data-val-required="Требуется поле Наименование риска." data-val="true">
                <span class="field-validation-error" data-valmsg-replace="true" data-valmsg-for="Name"><span for="Name" generated="true">Требуется поле Наименование риска.</span></span>
            </div>